Question

find the measures of the parts of the right triangle that are not given.
a 29° c 37 yd
c = □ yd
m∠b = □°
(round answers to the nearest whole number as needed.)

Explanation:

Step1: Find the measure of angle B

In a right - triangle, the sum of the interior angles is 180°. Since one angle is 90° and angle A = 29°, we use the formula \(m\angle A+m\angle B + m\angle C=180^{\circ}\), where \(m\angle C = 90^{\circ}\). So \(m\angle B=180^{\circ}-90^{\circ}-29^{\circ}\).
\[m\angle B = 61^{\circ}\]

Step2: Find the length of side c

We know the adjacent side to angle A (\(AC = 37\) yd) and we want to find the hypotenuse c. We use the cosine function \(\cos(A)=\frac{AC}{c}\), where \(A = 29^{\circ}\) and \(AC = 37\) yd. So \(c=\frac{37}{\cos(29^{\circ})}\).
\[c=\frac{37}{\cos(29^{\circ})}\approx\frac{37}{0.8746}\approx42\] (rounded to the nearest whole number)

Answer:

c = 42 yd
m∠B = 61°