Question

find the missing side.
13
x
32°
x = ?
round to the nearest tenth.
remember: sohcahtoa

Explanation:

Step1: Identify the trigonometric ratio

We use the sine ratio (\(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\)). Here, \(\theta = 32^{\circ}\), the opposite side is \(x\), and the hypotenuse is \(13\). So, \(\sin(32^{\circ})=\frac{x}{13}\).

Step2: Solve for \(x\)

Multiply both sides by \(13\): \(x = 13\times\sin(32^{\circ})\).
Using a calculator, \(\sin(32^{\circ})\approx0.5299\). Then \(x=13\times0.5299 = 6.8887\).

Step3: Round to the nearest tenth

Rounding \(6.8887\) to the nearest tenth gives \(6.9\).

Answer:

\(6.9\)