Question

In ΔLMN, the measure of ∠N=90°, the measure of ∠M=70°, and NL = 74 feet. Find the length of MN to the nearest tenth of a foot.

Answer 1

Answer:26.9 feet

Step-by-step explanation:

SOH-CAH-TOA

\tan M = \frac{\text{opposite}}{\text{adjacent}}=\frac{74}{x}

tanM=

adjacent

opposite

​

=

x

74

​

\tan 70=\frac{74}{x}

tan70=

x

74

​

x\tan 70=74

xtan70=74

Cross multiply.

\frac{x\tan 70}{\tan 70}=\frac{74}{\tan 70}

tan70

xtan70

​

=

tan70

74

​

Divide each side by tan 70.

x=\frac{74}{\tan 70}=26.9338\approx 26.9\text{ feet}

x=

tan70

74

​

=26.9338≈26.9 feet

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

L

M

N

74

26.9

(opposite of ∠M)

(adj. to ∠M)

(hypotenuse)

70°