Question

In AGHI, the measure of ZI=90°, the measure of ZG=82°, and GH = 3.4 feet. Find the length of HI to the nearest tenth of a foot. H 3.4 X 820 I I G

Answer 1

To find the value of the missing side we can use the trigonometric functions with the values of tha angle and the side given because its a righ triangle.

The corresponding trigonometric is the sin of 82° which involves the opposite side of the angle (x) and the hypotenuse

$\begin{gathered} \sin 82=\frac{x}{\text{hyp}} \\ \sin 82=\frac{x}{3.4} \\ x=3.4\sin 82 \\ x=3.3669 \\ x\cong3.4ft \end{gathered}$