In ΔEFG, the measure of ∠G=90°, the measure of ∠F=47°, and FG = 6.5 feet. Find the length of EF to the nearest tenth of a foot.

55

Step-by-step explanation:

9.5 feet

Step-by-step explanation:

What function uses the ADJACENT and the HYPOTENUSE?

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\cos F = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{6.5}{x}

cosF=

hypotenuse

adjacent

​

=

x

6.5

​

\cos 47=\frac{6.5}{x}

cos47=

x

6.5

​

x\cos 47=6.5

xcos47=6.5

Cross multiply.

\frac{x\cos 47}{\cos 47}=\frac{6.5}{\cos 47}

cos47

xcos47

​

=

cos47

6.5

​

Divide each side by cos 47.

x=\frac{6.5}{\cos 47}=9.5308\approx 9.5\text{ feet}

x=

cos47

6.5

​

=9.5308≈9.5 feet

correct

step-by-step explanation: