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°

Question

asked Dec 20, 2019 219k views

2 Answers

Kamel · Answer 1 · 2019-12-25T09:10:28+0000

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.