Question

use a trigonometric function to solve for x. round answer to the nearest tenth.
32.5
11.3
68.3
26.7

Explanation:

Step1: Identify trigonometric function

In a right triangle, the sine of an angle is defined as the ratio of the length of the opposite side to the hypotenuse. Here, angle is \(67^\circ\), hypotenuse is \(29\), and \(x\) is the opposite side to \(67^\circ\). So we use \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
\(\sin(67^\circ)=\frac{x}{29}\)

Step2: Solve for x

Multiply both sides by \(29\) to get \(x = 29\times\sin(67^\circ)\). Calculate \(\sin(67^\circ)\approx0.9205\). Then \(x\approx29\times0.9205\approx26.7\).

Answer:

26.7