{"id":1431,"date":"2019-03-14T07:21:36","date_gmt":"2019-03-14T06:21:36","guid":{"rendered":"https:\/\/www.nickzom.org\/blog\/?p=1431"},"modified":"2024-02-18T07:27:43","modified_gmt":"2024-02-18T06:27:43","slug":"how-to-apply-sine-rule-cosine-rule-and-tangent-rule-in-trigonometry","status":"publish","type":"post","link":"https:\/\/www.nickzom.org\/blog\/2019\/03\/14\/how-to-apply-sine-rule-cosine-rule-and-tangent-rule-in-trigonometry\/","title":{"rendered":"How to Apply Sine Rule, Cosine Rule and Tangent Rule in Trigonometry"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Navigating the complexities of trigonometry becomes simpler with a firm grasp of the fundamental rule that guides Sine, Cosine, and Tangent. In this article, we delve into practical applications of these rules, exploring how they facilitate solving triangles, determining unknown sides and angles, and unraveling geometric puzzles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mastering these rules equips you with the knowledge to tackle diverse trigonometric problems effectively.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Sine Rule<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In trigonometry, the sine law, law of sines, sine rule, or sine formula is a rational equation that relates to the lengths of the sides of a triangle (any shape or kind) to the sines of its angles.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">According to the sine rule,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong><sup>a<\/sup> \/ <sub>sin(A)<\/sub> = <sup>b<\/sup> \/ <sub>sin(B)<\/sub> = <sup>c<\/sup> \/ <sub>sin(C)<\/sub><\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"561\" height=\"378\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/sinerule.png\" alt=\"How to Apply Sine Rule, Cosine Rule and Tangent Rule in Trigonometry\" class=\"wp-image-1432\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/sinerule.png 561w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/sinerule-300x202.png 300w\" sizes=\"(max-width: 561px) 100vw, 561px\" \/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\"><strong><u>Application of Sine Rule<\/u><\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Sine rule can be used to find the unknown side or length of a triangle.<\/li>\n\n\n\n<li>Sine rule can also be used to find the unknown angle of a triangle.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>To find the unknown side or length of a triangle, three essential parameters must be provided and these parameters are:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The angle opposite to the unknown side or length of the triangle.<\/li>\n\n\n\n<li>The length of a side of the triangle (b).<\/li>\n\n\n\n<li>Then, the angle opposite to the length of the side (b) of the triangle.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s take for example we have a triangle and we want to determine the unknown side of this triangle, when the opposite angle is given, another length of the side of the triangle and its opposite angle is also given. Like the image below.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"542\" height=\"436\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/unknownside-sine.gif\" alt=\"How to Apply Sine Rule, Cosine Rule and Tangent Rule in Trigonometry\" class=\"wp-image-1433\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">From the image above, one can see that;<br>The angle opposite to the unknown length of the side of the triangle is 80\u00b0. (A)<br>The length of the side of the triangle given is 7. (b)<br>Also, the angle opposite to the length of the side of the triangle given is 60\u00b0 (B)<br>The unknown length of the side of the triangle is x. (a)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Applying the sine rule to find the value of x:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>a<\/sup> \/ <sub>sin(A)<\/sub> = <sup>b<\/sup> \/ <sub>sin(B)<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>x<\/sup> \/ <sub>sin(80\u00b0)<\/sub> = <sup>7<\/sup> \/ <sub>sin(60\u00b0)<\/sub><br><sup>x<\/sup> \/ <sub>0.9848<\/sub> = <sup>7<\/sup> \/ <sub>0.8660<\/sub><\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Applying <b>cross multiplication<\/b><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">So, x (0.8660) = 7 (0.9848)<br>x (0.8660) = 6.8936<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dividing both sides by 0.8660<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x = <sup>6.8936<\/sup> \/ <sub>0.8660<\/sub><br>x = 7.96<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the unknown length of the side of the triangle, x is 7.96.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Read more:&nbsp;<a href=\"https:\/\/www.nickzom.org\/blog\/2018\/12\/29\/how-to-calculate-and-solve-for-the-area-base-and-height-of-a-triangle-the-calculator-encyclopedia\/\">How to Calculate and Solve for the Area, Base and Height of a Triangle | The Calculator Encyclopedia<\/a><\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Using the Sine Rule When the Angle of a Triangle is Unknown<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s try to solve another example using the sine rule where the angle of a triangle is unknown, the opposite length of the side is given and another angle and its opposite side is also given.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"778\" height=\"406\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/unknownangle-sine.gif\" alt=\"\" class=\"wp-image-1530\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>a<\/sup> \/ <sub>sin(A)<\/sub> = <sup>b<\/sup> \/ <sub>sin(B)<\/sub><br>Let the unknown angle be B\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore,<br>a = 5.1<br>A = 100\u00b0<br>b = 3.6<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where a and b represent the length of the side of the triangle and A and B represent the angle of the triangle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>5.1<\/sup> \/ <sub>sin(100\u00b0)<\/sub> = <sup>3.6<\/sup> \/ <sub>sin(B\u00b0)<\/sub><br><sup>5.1<\/sup> \/ <sub>(0.9848)<\/sub> = <sup>3.6<\/sup> \/ <sub>sin(B\u00b0)<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">That is, 5.1 x sin(B\u00b0) = 3.6 x 0.9848<br>5.1 x sin(B\u00b0) = 3.5453<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">sin(B\u00b0) = <sup>3.5453<\/sup> \/ <sub>5.1<\/sub><br>sin(B\u00b0) = 0.6951<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B = sin<sup>-1<\/sup>(0.6951)<br>B = 44.04\u00b0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Cosine Rule<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The cosine rule provides a relationship between the lengths of the sides a triangle to the cosine of its opposite angles.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"371\" height=\"357\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/cosine-rule.png\" alt=\"How to Apply Sine Rule, Cosine Rule and Tangent Rule in Trigonometry\" class=\"wp-image-1531\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/cosine-rule.png 371w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/cosine-rule-300x289.png 300w\" sizes=\"(max-width: 371px) 100vw, 371px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Just as is in the image, the cosine rule relates the length, <strong>a<\/strong> to its opposite angle, <strong>A<\/strong>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a\u00b2 = b\u00b2 + c\u00b2 &#8211; 2bc . cos(A\u00b0)<br>b\u00b2 = a\u00b2 + c\u00b2 &#8211; 2ac . cos(B\u00b0)<br>c\u00b2 = a\u00b2 + b\u00b2 &#8211; 2ab . cos(C\u00b0)<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Applications of Cosine Rule<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cosine rule can be used to calculate the three angles of a triangle provided the lengths of its three sides are provided.<\/li>\n\n\n\n<li>Cosine rule can be used to calculate the length of a side of a triangle.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Now, let&#8217;s see an example of how one can use cosine rule to compute the three angles of a triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"512\" height=\"286\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/cosinerule-allangles.gif\" alt=\"\" class=\"wp-image-1532\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s assume that<br>a = 5.9<br>b = 3.1<br>c = 4.3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We would first of all calculate for angle A\u00b0<br>from the formulas above we know that;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a\u00b2 = b\u00b2 + c\u00b2 &#8211; 2bc . cos(A\u00b0)<br>2bc . cos(A\u00b0) = b\u00b2 + c\u00b2 &#8211; a\u00b2<br>cos(A\u00b0) = <sup>(b\u00b2 + c\u00b2 &#8211; a\u00b2)<\/sup> \/ <sub>2bc<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entering the Values<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">cos(A\u00b0) = <sup>((3.1)\u00b2 + (4.3)\u00b2 &#8211; (5.9)\u00b2)<\/sup> \/ <sub>2(3.1)(4.3)<\/sub><br>cos(A\u00b0) = <sup>(9.61 + 18.49 &#8211; 34.81)<\/sup> \/ <sub>26.66<\/sub><br>That is, cos(A\u00b0) = <sup>-8.71<\/sup> \/ <sub>26.66<\/sub><br>cos(A\u00b0) = -0.2517<br>A = cos<sup>-1<\/sup>(-0.2517)<br>A = 104.58\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Calculating for angle, B\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b\u00b2 = a\u00b2 + c\u00b2 &#8211; 2ac . cos(B\u00b0)<br>2ac . cos(B\u00b0) = a\u00b2 + c\u00b2 &#8211; b\u00b2<br>cos(B\u00b0) = <sup>(a\u00b2 + c\u00b2 &#8211; b\u00b2)<\/sup> \/ <sub>2ac<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entering the Values<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">cos(B\u00b0) = <sup>((5.9)\u00b2 + (4.3)\u00b2 &#8211; (3.1)\u00b2)<\/sup> \/ <sub>2(5.9)(4.3)<\/sub><br>cos(B\u00b0) = <sup>(34.81 + 18.49 &#8211; 9.61)<\/sup> \/ <sub>50.74<\/sub><br>So, cos(B\u00b0) = <sup>43.69<\/sup> \/ <sub>50.74<\/sub><br>cos(B\u00b0) = 0.8611<br>B = cos<sup>-1<\/sup>(0.8611)<br>B = 30.56\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Calculating for angle, C\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">c\u00b2 = a\u00b2 + b\u00b2 &#8211; 2ab . cos(C\u00b0)<br>2ab . cos(C\u00b0) = a\u00b2 + b\u00b2 &#8211; c\u00b2<br>cos(C\u00b0) = <sup>(a\u00b2 + b\u00b2 &#8211; c\u00b2)<\/sup> \/ <sub>2ab<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Entering the Values<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">cos(C\u00b0) = <sup>((5.9)\u00b2 + (3.1)\u00b0 &#8211; (4.3)\u00b0)<\/sup> \/ <sub>2(5.9)(3.1)<\/sub><br>cos(C\u00b0) = <sup>(34.81 + 9.61 &#8211; 18.49)<\/sup> \/ <sub>36.58<\/sub><br>Then, cos(C\u00b0) = <sup>25.93<\/sup> \/ <sub>36.58<\/sub><br>cos(C\u00b0) = 0.7089<br>C = cos<sup>-1<\/sup>(0.7089)<br>C = 44.86\u00b0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Side of a Triangle When the Two Sides are Given<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Now, let&#8217;s calculate the length of the side of a triangle when the two other sides are given and the opposite angle of the unknown length is also given.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"512\" height=\"262\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/cosine-rule-1.png\" alt=\"\" class=\"wp-image-1540\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/cosine-rule-1.png 512w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/cosine-rule-1-300x154.png 300w\" sizes=\"(max-width: 512px) 100vw, 512px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">From our cosine formulas:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b\u00b2 = a\u00b2 + c\u00b2 &#8211; 2ac . cos(B\u00b0)<br>where:<br>a = 26<br>c = 18<br>B = 26\u00b0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b\u00b2 = (26)\u00b2 + (18)\u00b2 &#8211; 2(26)(18) . cos(26\u00b0)<br>b\u00b2 = 676 + 324 &#8211; 2(468) . (0.8987)<br>So, b\u00b2 = 1000 &#8211; 841.2712<br>b\u00b2 = 158.7287<br>b = \u221a(158.7287)<br>Therefore, b = 12.599<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Tangent Rule<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The tangent rule relates the tangents of two angles to the length of the opposite sides of the triangle.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"1024\" height=\"614\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/tangent-1024x614.png\" alt=\"How to Apply Sine Rule, Cosine Rule and Tangent Rule in Trigonometry\" class=\"wp-image-1543\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/tangent-1024x614.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/tangent-300x180.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/tangent-768x461.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/tangent.png 1200w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>(a &#8211; b)<\/sup> \/ <sub>(a + b)<\/sub> = <sup>tan(A &#8211; B)<\/sup> \/ <sub>tan(A + B)<\/sub><br>Let&#8217;s assume;<br>b = 10<br>A = 70\u00b0<br>B = 20\u00b0<br>How can we find the length of side a?<br>We make use of the <b>tangent rule<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>(a &#8211; 10)<\/sup> \/ <sub>(a + 10)<\/sub> = <sup>(tan(0.5(70\u00b0 &#8211; 20\u00b0)))<\/sup> \/ <sub>(tan(0.5(70\u00b0 + 20\u00b0)))<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>(a &#8211; 10)<\/sup> \/ <sub>(a + 10)<\/sub> = <sup>(tan(0.5(50\u00b0)))<\/sup> \/ <sub>(tan(0.5(90\u00b0)))<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>(a &#8211; 10)<\/sup> \/ <sub>(a + 10)<\/sub> = <sup>(tan(25\u00b0))<\/sup> \/ <sub>(tan(45\u00b0))<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>(a &#8211; 10)<\/sup> \/ <sub>(a + 10)<\/sub> = <sup>(0.4663076581549986)<\/sup> \/ <sub>(0.9999999999999999)<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Then,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><sup>(a &#8211; 10)<\/sup> \/ <sub>(a + 10)<\/sub> = 0.46630765815499864<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(a &#8211; 10) = 0.46630765815499864(a + 10)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, a &#8211; 10 = 0.46630765815499864a + 4.663076581549986<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a &#8211; 0.46630765815499864a = 10 + 4.663076581549986<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">0.5336923418450014a = 14.663076581549987<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a = <sup>14.663076581549987<\/sup> \/ <sub>0.5336923418450014<\/sub><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a = 27.474774194546228<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, a = 27.47<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Always, remember to add length units whenever you are done calculating the length of a side of a triangle.<br>For Example: the length of the side a of the triangle from the calculation above is 27.47 metres.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Using Nickzom Calculator to Apply Sine Rule, Cosine Rule and Tangent Rule in Trigonometry<\/strong><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Nickzom Calculator \u2013&nbsp;<strong>The Calculator Encyclopedia<\/strong> is capable of calculating problems on sine rule, cosine rule and tangent rule.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To get the answer and workings of calculations on sine rule, cosine rule and tangent rule using the <strong>Nickzom Calculator \u2013 The Calculator Encyclopedia.\u00a0<\/strong>First, you need to obtain the app.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Access the Nickzom Calculator<\/strong><\/h4>\n\n\n\n<p class=\"wp-block-paragraph\">You can get this app via any of these means:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Web<\/strong>&nbsp;\u2013&nbsp;<a href=\"https:\/\/www.nickzom.org\/calculator-plus\">https:\/\/www.nickzom.org\/calculator-plus<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To get access to the&nbsp;<strong>professional&nbsp;<\/strong>version via web, you need to&nbsp;<strong>register<\/strong>&nbsp;and&nbsp;<strong>subscribe&nbsp;<\/strong>for<strong>&nbsp;NGN 1,500&nbsp;<\/strong>per<strong>&nbsp;annum<\/strong>&nbsp;to have utter access to all functionalities.<br>You can also try the&nbsp;<strong>demo&nbsp;<\/strong>version via&nbsp;<a href=\"https:\/\/www.nickzom.org\/calculator\">https:\/\/www.nickzom.org\/calculator<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Android (Paid)<\/strong>&nbsp;\u2013&nbsp;<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=org.nickzom.nickzomcalculator<\/a><br><strong>Android (Free)<\/strong>&nbsp;\u2013&nbsp;<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator\">https:\/\/play.google.com\/store\/apps\/details?id=com.nickzom.nickzomcalculator<\/a><br><strong>Apple (Paid)<\/strong>&nbsp;\u2013&nbsp;<a href=\"https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8\">https:\/\/itunes.apple.com\/us\/app\/nickzom-calculator\/id1331162702?mt=8<\/a><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Once, you have obtained the calculator encyclopedia app, proceed to the&nbsp;<strong>Calculator Map,&nbsp;<\/strong>you can either click on the cosine rule, sine rule, or tangent rule under Mathematics to solve any trigonometry calculations in need of such relationship.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"1024\" height=\"546\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Capture-1024x546.png\" alt=\"How to Apply Sine Rule, Cosine Rule and Tangent Rule in Trigonometry\" class=\"wp-image-1544\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Capture-1024x546.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Capture-300x160.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Capture-768x409.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Capture.png 1366w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Displaying an example of how Nickzom Calculator solves for tangent rule.<br>First click on tangent rule, then enter the required parameters.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-646-1024x576.png\" alt=\"\" class=\"wp-image-1545\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-646-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-646-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-646-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-646.png 1366w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, click on <strong>Calculate<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-647-1024x576.png\" alt=\"\" class=\"wp-image-1546\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-647-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-647-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-647-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-647.png 1366w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"1024\" height=\"576\" src=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-648-1024x576.png\" alt=\"\" class=\"wp-image-1547\" srcset=\"https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-648-1024x576.png 1024w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-648-300x169.png 300w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-648-768x432.png 768w, https:\/\/www.nickzom.org\/blog\/wp-content\/uploads\/2019\/03\/Screenshot-648.png 1366w\" sizes=\"(max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">As you can see from the screenshot above,\u00a0<strong>Nickzom Calculator<\/strong> \u2013 The Calculator Encyclopedia solves for the length of the side of a using the <strong>tangent rule<\/strong> and can also solve for the three angles of a triangle and the length of the side of a triangle using the cosine rule and also the length of a side of a triangle and angle of a triangle using sine rule and presents the formula, workings, and steps too.<\/p>\n","protected":false},"excerpt":{"rendered":"Navigating the complexities of trigonometry becomes simpler with a firm grasp of the fundamental rule that guides Sine,&hellip;","protected":false},"author":1,"featured_media":12761,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_opengraph-title":"","_yoast_wpseo_opengraph-description":"","_yoast_wpseo_twitter-title":"","_yoast_wpseo_twitter-description":"","_lmt_disableupdate":"","_lmt_disable":"","_sitemap_exclude":false,"_sitemap_priority":"","_sitemap_frequency":"","_yoast_wpseo_focuskw_text_input":"","csco_display_header_overlay":false,"csco_singular_sidebar":"","csco_page_header_type":"","footnotes":""},"categories":[4],"tags":[385,84,478,505,475,506,169,56,87,476,481,474,477,479,480],"class_list":["post-1431","post","type-post","status-publish","format-standard","has-post-thumbnail","category-mathematics","tag-angle","tag-calculator-encyclopedia","tag-cosine-rule","tag-law-of-cosines","tag-law-of-sines","tag-law-of-tangents","tag-length","tag-mathematics","tag-nickzom-calculator","tag-sine-forumla","tag-sine-law","tag-sine-rule","tag-sines-of-angles","tag-tangent-rule","tag-trigonometry","cs-entry"],"yoast_head":"<!-- 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