In ΔFGH, the measure of ∠H=90°, the measure of ∠G=21°, and FG= 9 feet. Find the length of GH to the nearest tenth of a foot.

8.4 feet

Step-by-step explanation:

In ΔFGH, the measure of ∠H=90°, the measure of ∠G=21°, and FG = 9 feet. Find the length of GH to the nearest tenth of a foot.

F

G

H

x

9

(opposite of ∠G)

(adj. to ∠G)

(hypotenuse)

21°

\text{What function uses the HYPOTENUSE and the ADJACENT?}

What function uses the HYPOTENUSE and the ADJACENT?

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\cos G = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{x}{9}

cosG=  

hypotenuse

adjacent

=  

9

x

\cos 21=\frac{x}{9}

cos21=  

9

x

9\cos 21=x

9cos21=x

Cross multiply.

x=8.4022\approx \mathbf{8.4}\text{ feet}

x=8.4022≈8.4 feet

Type into calculator and roundto the nearest tenth of a foot.

F

G

H

8.4

9

(opposite of ∠G)

(adj. to ∠G)

(hypotenuse)

21°