Question

follow the steps to find the area of the shaded region. next, find the height (h) of the triangle inside the sector. hint: use sohcahtoa h = ? cm round to four decimal places

Explanation:

Step1: Identify the sine - function relationship

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the angle $\theta = 46^{\circ}$, the hypotenuse of the right - triangle is $r = 14$ cm, and the height $h$ is the side opposite to the angle $\theta$.
So, $\sin(46^{\circ})=\frac{h}{14}$.

Step2: Solve for $h$

Multiply both sides of the equation $\sin(46^{\circ})=\frac{h}{14}$ by 14. We get $h = 14\times\sin(46^{\circ})$.
Since $\sin(46^{\circ})\approx0.7193$, then $h=14\times0.7193 = 10.0702$ cm.

Answer:

$10.0702$