Question

Given right triangle MNL, what is the value of cos(M)?

A. 3/5
B. 3/4
C. 4/5
D. 5/3

Answer 1

The correct answer is option C. 4/5

Explanation:

Pythagorean theorem:-

Hypotenuse² = Base² + Height²

It is given a right triangle ABC.

To find the value of MN

Hypotenuse² = Base² + Height²

ML = 25

NL =15

MN = ?

ML² = NL² + MN²

MN² = ML² - NL² = 25² - 15² = 625 - 225 = 400

MN = √400 = 20

To find Cos(M)

Cos(M) = Adjacent side/Hypotenuse

Cos(M) = MN/ML= 20/25 = 4/5

The correct answer is Option C. 4/5

Answer 2

C. 4/5

Explanation:

We have that cos(M) = Adjacent side/Hypotenuse

Where:

Hypotenuse (h) = 25

We do not know the adjacent side (a), but the opposite side (b).

Then we use the Pythagorean theorem:

`h ^ 2 = a ^ 2 + b ^ 2\\a ^ 2 = -b ^ 2 + h ^ 2\\a ^ 2 = -15 ^ 2 + 25 ^ 2\\a ^ 2 = 400\\a = 20`

Then:

`cos(M) = (20)/(25) = (4)/(5)`

Option C