Question

In ΔLMN, the measure of ∠N=90°, MN = 8.6 feet, and NL = 6.4 feet. Find the measure of ∠M to the nearest degree.

Answer 1

`M \approx 37^(\circ)`

Explanation:

The value of angle M can be found with the help of trigonometric functions. Since
`\triangle LMN` is a right-angle triangle and both known sides are legs, the tangent function is used:

`\tan M = (6.4\,ft)/(8.6\,ft)`

`\tan M = 0.744`

`M = \tan^(-1) 0.744`

`M \approx 36.649^(\circ)`

`M \approx 37^(\circ)`

Answer 2

37°

Explanation:

Find the detailed diagram of the triangle in the attachment below.

Using the SOH, CAH TOA trigonometry ratio to get the angle M.

NL will be the opposite since it's facing the angle M that we are looking for, and side MN will be the adjacent side.

Using TOA;

tan ∠M= opposite/adjacent

tan∠M = NL/MN

tan∠M = 6.4/8.6

tan∠M= 0.7442

∠M= arctan 0.7442

∠M = 36.66°

∠M = 37° (to the nearest degree)