Question

use trig to find the value of each variable. round your answer to the nearest tenth. **remember to change to degrees setup: =

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine function is defined as \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 46^{\circ}\), the side opposite to the \(46^{\circ}\) angle is \(8\), and the hypotenuse is \(x\). So, the setup is \(\sin(46^{\circ})=\frac{8}{x}\).

Step2: Solve for \(x\)

Cross - multiply the equation \(\sin(46^{\circ})=\frac{8}{x}\) to get \(x\sin(46^{\circ}) = 8\). Then, \(x=\frac{8}{\sin(46^{\circ})}\).
We know that \(\sin(46^{\circ})\approx0.7193\) (using a calculator in degree mode).
So, \(x=\frac{8}{0.7193}\approx11.1\).

Answer:

setup: \(\sin(46^{\circ})=\frac{8}{x}\), \(x\approx11.1\)