Question

In ΔCDE, the measure of ∠E=90°, the measure of ∠C=17°, and EC = 74 feet. Find the length of CD to the nearest tenth of a foot

Answer 1

77.4 feet

Explanation:

\text{SOH-CAH-TOA}

SOH-CAH-TOA

\cos C = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{74}{x}

cosC=

hypotenuse

adjacent

​

=

x

74

​

\cos 17=\frac{74}{x}

cos17=

x

74

​

x\cos 17=74

xcos17=74

Cross multiply.

\frac{x\cos 17}{\cos 17}=\frac{74}{\cos 17}

cos17

xcos17

​

=

cos17

74

​

Divide each side by cos 17.

x=\frac{74}{\cos 17}=77.3812\approx 77.4\text{ feet}

x=

cos17

74

​

=77.3812≈77.4 feet