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: Recall the sine function

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

Step2: Calculate the height

Using the formula $\sin\theta=\frac{h}{14}$ (since $\text{opposite}=h$ and $\text{hypotenuse} = 14$), we can solve for $h$. So, $h = 14\times\sin(46^{\circ})$.
We know that $\sin(46^{\circ})\approx0.7193398$. Then $h = 14\times0.7193398=10.0707572$.

Answer:

$10.0708$