Question

follow the steps to find the area of the shaded region. use trigonometry to find the height of the triangle. hint: use sohcahtoa h = ? cm

Explanation:

Step1: Identify the relevant trig - ratio

We know the hypotenuse of the right - triangle (the radius of the circle, $r = 8$ cm) and we want to find the height $h$ of the triangle. The angle between the base and the hypotenuse is $51^{\circ}$. Since $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, and the height $h$ is the side opposite to the $51^{\circ}$ angle and the hypotenuse $c = 8$ cm.
$\sin\theta=\sin(51^{\circ})=\frac{h}{8}$

Step2: Solve for $h$

Multiply both sides of the equation $\sin(51^{\circ})=\frac{h}{8}$ by 8.
$h = 8\times\sin(51^{\circ})$
We know that $\sin(51^{\circ})\approx0.777$.
$h=8\times0.777 = 6.216$ cm

Answer:

$6.216$ cm