Question

use the right triangle and the given information to solve the triangle
( b = 9 ), ( b = 29 ^ { circ } ), find a, c, and a
( a = square ) (round to the nearest hundredth as needed )

Explanation:

Step1: Find angle \(A\)

In a right - triangle, \(A + B=90^{\circ}\). Given \(B = 29^{\circ}\), then \(A=90^{\circ}-B\).
\(A = 90^{\circ}-29^{\circ}=61^{\circ}\)

Step2: Find side \(a\)

We know that \(\tan B=\frac{b}{a}\). Given \(b = 9\) and \(B = 29^{\circ}\), then \(a=\frac{b}{\tan B}\).
\(a=\frac{9}{\tan(29^{\circ})}\)
Since \(\tan(29^{\circ})\approx0.5543\), \(a=\frac{9}{0.5543}\approx16.24\)

Step3: Find side \(c\)

We know that \(\sin B=\frac{b}{c}\). Then \(c=\frac{b}{\sin B}\).
Given \(b = 9\) and \(B = 29^{\circ}\), and \(\sin(29^{\circ})\approx0.4848\)
\(c=\frac{9}{0.4848}\approx18.56\)

Answer:

\(a\approx16.24\), \(c\approx18.56\), \(A = 61^{\circ}\)