Question

In ΔFGH, the measure of ∠H=90°, the measure of ∠G=85°, and GH = 4.5 feet. Find the length of FG to the nearest tenth of a foot.

Answer 1

51.6 feet

Explanation:

\cos G = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{4.5}{x}

cosG=

hypotenuse

adjacent

​

=

x

4.5

​

\cos 85=\frac{4.5}{x}

cos85=

x

4.5

​

x\cos 85=4.5

xcos85=4.5

Cross multiply.

\frac{x\cos 85}{\cos 85}=\frac{4.5}{\cos 85}

cos85

xcos85

​

=

cos85

4.5

​

Divide each side by cos 85.

x=\frac{4.5}{\cos 85}=51.6317\approx 51.6\text{ feet}

x=

cos85

4.5

​

=51.6317≈51.6 feet