Question

given right triangle mnl, what is the value of cos(m)?

Explanation:

Step1: Recall cosine - ratio definition

In a right - triangle, $\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$. For $\angle M$, the adjacent side to $\angle M$ needs to be found first. Using the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 25$ (hypotenuse) and $b = 15$ (one of the legs). Let the adjacent side to $\angle M$ be $a$. Then $a=\sqrt{c^{2}-b^{2}}$.

Step2: Calculate the adjacent side

$a=\sqrt{25^{2}-15^{2}}=\sqrt{(25 + 15)(25 - 15)}=\sqrt{40\times10}=\sqrt{400}=20$.

Step3: Calculate $\cos(M)$

$\cos(M)=\frac{\text{adjacent to }M}{\text{hypotenuse}}=\frac{20}{25}=\frac{4}{5}$.

Answer:

$\frac{4}{5}$