Question

find the measures of the parts of the right triangle that are not given.

Explanation:

Step1: Find angle B

In a right - triangle, the sum of the interior angles is 180°. Since one angle is 90° and angle A = 29°, then angle B=180° - 90° - 29° = 61°. But we are mainly focused on side - length calculations here.

Step2: Find side a

We know that $\tan A=\frac{a}{AC}$. Given $A = 29^{\circ}$ and $AC = 37$ yd. So $a=AC\times\tan A$. Substituting the values, $a = 37\times\tan(29^{\circ})$. Using a calculator, $\tan(29^{\circ})\approx0.5543$, then $a = 37\times0.5543\approx20.51$ yd.

Step3: Find side c

We know that $\cos A=\frac{AC}{c}$. So $c=\frac{AC}{\cos A}$. Given $A = 29^{\circ}$ and $AC = 37$ yd. $\cos(29^{\circ})\approx0.8746$. Then $c=\frac{37}{0.8746}\approx42.30$ yd.

Answer:

$a\approx20.51$ yd
$c\approx42.30$ yd