Question

solve for x.
15 cm
35°
x =? cm
round to the nearest hundredth.

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 35^{\circ}\), the hypotenuse is \(15\) cm and the opposite side is \(x\). So, \(\sin(35^{\circ})=\frac{x}{15}\).

Step2: Solve for \(x\)

Multiply both sides of the equation \(\sin(35^{\circ})=\frac{x}{15}\) by \(15\). We get \(x = 15\times\sin(35^{\circ})\). Since \(\sin(35^{\circ})\approx0.5736\), then \(x=15\times0.5736 = 8.604\approx8.60\) (rounded to the nearest hundredth).

Answer:

\(8.60\)