Solve the triangle:

Question:

Solve the triangle:

Trigonometric Ratios:

The trigonometric ratios are used to find the length and the angle of the right angle and non-right angled triangles. The length sol found for each side of the triangle are termed as the solution of the given triangle

Answer and Explanation:


We will first mark the vertex of the triangle as shown in the figure below:


Figure


Now we use the trigonometric ratios to get the other sides of the triangle:

{eq}\displaystyle \tan 37^{\circ \:}= \frac{46}{BC}\\ \displaystyle \Rightarrow BC=\frac{46}{\tan \left(37^{\circ \:}\right)}=61.04\\ {/eq}

Also we have:

{eq}\displaystyle \sin 37^{\circ \:}= \frac{46}{AB}\\ \displaystyle \Rightarrow AB=\frac{46}{\sin \left(37^{\circ \:}\right)}=76.4354\\ {/eq}

So this is the solution of the given triangle.


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Trigonometric Ratios and Similarity

from Geometry: High School

Chapter 14 / Lesson 7
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