Question

solve for x.
10 cm
37°
x =? cm
round to the nearest hundredth.

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 37^{\circ}\), the hypotenuse is \(10\) cm and the opposite side is \(x\). So, \(\sin(37^{\circ})=\frac{x}{10}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(37^{\circ})=\frac{x}{10}\) by \(10\). We get \(x = 10\times\sin(37^{\circ})\). Since \(\sin(37^{\circ})\approx0.6018\), then \(x=10\times0.6018 = 6.018\approx6.02\) (rounded to the nearest hundredth).

Answer:

\(6.02\)