Question

In `Delta`LMN, `/_N` is a right angle, LM = 76, and MN = 40. What is m`/_M` ?

a. 28°
b. 32°
c. 40°
d. 58°

Answer 1

The answer is D. 58 degrees.....I just finished this test so I know this is correct

Answer 2

Please find the attachment for a complete understanding of the solution provided here.

As can be seen from the diagram, the hypotenuse, LM is 76 and the base, MN is 40. We have to find the angle M.

From basic trigonometry we know that

`Cos \theta=(Base)/(Hypotenuse)`

Thus, in our case, we will have,
`\theta` as
`\angle M` and thus, the above equation will modify as:

`Cos(\angle M)=(Base)/(Hypotenuse) =(40)/(76)`

Therefore,
`\angle M=Cos^(-1) ((40)/(76) ) \approx 58.24^(0)`

Thus out of the given options, option D is the closest to the answer we got.