Question

what is the value of x to the nearest tenth?
29.6
x
73°
33°
x =

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(A\). Then \(A = 180^{\circ}-73^{\circ}-33^{\circ}=74^{\circ}\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Here, if we consider \(a = 29.6\), \(A = 74^{\circ}\), \(B = 33^{\circ}\), and \(b=x\). So \(\frac{29.6}{\sin74^{\circ}}=\frac{x}{\sin33^{\circ}}\).

Step3: Solve for \(x\)

We know that \(\sin74^{\circ}\approx0.961\) and \(\sin33^{\circ}\approx0.545\). Then \(x=\frac{29.6\times\sin33^{\circ}}{\sin74^{\circ}}\). Substitute the values: \(x=\frac{29.6\times0.545}{0.961}\).
\(x=\frac{16.132}{0.961}\approx16.8\)

Answer:

\(16.8\)