Question

use a calculator to find the length of each side to four decimal places.
notice the right triangle gives the measure of an angle and the length of the leg opposite hypotenuse? is the calculator set in degree or radian mode?
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determine length of right triangle side
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Explanation:

Step1: Find side \(b\) using tangent function

We know that \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here \(\theta = 62^{\circ}\), the adjacent - side to the \(62^{\circ}\) angle is \(b\) and the opposite - side is \(13\). So \(\tan62^{\circ}=\frac{13}{b}\), then \(b=\frac{13}{\tan62^{\circ}}\). Using a calculator in degree mode, \(b=\frac{13}{\tan62^{\circ}}\approx6.1031\).

Step2: Find side \(a\) using cosine function

We know that \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 62^{\circ}\), the adjacent - side to the \(62^{\circ}\) angle is \(b\approx6.1031\) and the hypotenuse is \(a\). So \(\cos62^{\circ}=\frac{b}{a}\), then \(a = \frac{b}{\cos62^{\circ}}\). Substituting \(b\approx6.1031\) into the formula, \(a=\frac{6.1031}{\cos62^{\circ}}\approx13.0000\).

Answer:

\(a\approx13.0000\), \(b\approx6.1031\)