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 round to four decimal places.

Explanation:

Step1: Recall the sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, the hypotenuse is \(8\) cm and \(\theta = 51^{\circ}\), and the height \(h\) is the side opposite to the angle \(51^{\circ}\).

Step2: Apply the sine formula

Using the formula \(h = 8\times\sin(51^{\circ})\).
We know that \(\sin(51^{\circ})\approx0.7771\) (using a calculator).
So, \(h = 8\times0.7771\).

Answer:

\(h = 6.2168\) cm