Question

use the triangle shown on the right to answer the question. which equation can you use to solve for a?
( \frac{a}{sin (35^{circ})}=\frac{30}{sin (35^{circ})} )
( \frac{a}{sin (35^{circ})}=\frac{30}{sin (60^{circ})} )
( \frac{a}{sin (85^{circ})}=\frac{30}{sin (35^{circ})} )
complete
a
17.2
19.9
34.5
52.1

Explanation:

Step1: Find angle \( B \)

By the angle - sum property of a triangle (\( A + B + C=180^{\circ} \)), \( B = 180^{\circ}-35^{\circ}-85^{\circ}=60^{\circ} \)

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Here, \(a\) is opposite angle \(A = 35^{\circ}\), and the side of length \(30\) is opposite angle \(B = 60^{\circ}\). So, \(\frac{a}{\sin(35^{\circ})}=\frac{30}{\sin(60^{\circ})}\)

Answer:

\(\frac{a}{\sin(35^{\circ})}=\frac{30}{\sin(60^{\circ})}\)