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})} )

Explanation:

Step1: Use the Law of Sines

The Law of Sines states that in any triangle \(ABC\) with sides \(a\), \(b\), \(c\) opposite angles \(A\), \(B\), \(C\) respectively, \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\).
In the given triangle, side \(a\) is opposite the \(35^{\circ}\) angle (angle \(A\)), and the side of length \(30\) is opposite the \(60^{\circ}\) angle (since \(180^{\circ}-35^{\circ}-85^{\circ} = 60^{\circ}\), using the angle - sum property of a triangle \(A + B+C=180^{\circ}\)).

Step2: Apply the Law of Sines formula

By the Law of Sines, \(\frac{a}{\sin(35^{\circ})}=\frac{30}{\sin(60^{\circ})}\)

Answer:

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