Question

given right triangle mnl, what is the value of cos(m)?
$\frac{3}{5}$
$\frac{3}{4}$
$\frac{4}{5}$
$\frac{5}{3}$

Explanation:

Step1: Find side MN via Pythagoras

For right triangle $MNL$ (right at $N$), use Pythagorean theorem: $MN^2 + NL^2 = ML^2$.
$$MN = \sqrt{ML^2 - NL^2} = \sqrt{25^2 - 15^2} = \sqrt{625 - 225} = \sqrt{400} = 20$$

Step2: Apply cosine definition for $\angle M$

Cosine of an angle in right triangle is $\frac{\text{adjacent side}}{\text{hypotenuse}}$. For $\angle M$, adjacent side is $MN=20$, hypotenuse is $ML=25$.
$$\cos(M) = \frac{MN}{ML} = \frac{20}{25} = \frac{4}{5}$$

Answer:

$\boldsymbol{\frac{4}{5}}$ (Option C: $\frac{4}{5}$)