Question

In ΔKLM, the measure of ∠M=90°, the measure of ∠L=31°, and MK = 7 feet. Find the length of LM to the nearest tenth of a foot.

Answer 1

11.6 feet

Explanation:

-ΔKLM is a right angle triangle.

-The missing ∠K=90-31=59° and it corresponds to length LM

-We apply the Law of Sines to determine the length LM:

`(a)/(Sin \ A)=(b)/(Sin \ B)\\\\(LM)/(Sin \ 59\textdegree)=(7)/(Sin\ 31\textdegree)\\\\LM=(7\ Sin 59\textdegree)/(Sin \ 31 \textdegree)\\\\=11.65\approx11.6\ ft`

Hence, LM has a length of 11.6 feet.