Question

fall 2025 geometry b wwva trigonometric ratios given right triangle mnl, what is the value of cos(m)?

Explanation:

Step1: Recall cosine ratio formula

$\cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}}$

Step2: Identify sides for angle M

For $\angle M$ in right - triangle $MNL$, the adjacent side to $\angle M$ is $MN$ and the hypotenuse is $ML$. First, find $MN$ using the Pythagorean theorem. Let $MN = x$, then $x^{2}+15^{2}=25^{2}$, so $x^{2}=25^{2}-15^{2}=(25 + 15)(25 - 15)=40\times10 = 400$, and $x = 20$.

Step3: Calculate cos(M)

$\cos(M)=\frac{MN}{ML}=\frac{20}{25}=\frac{4}{5}$

Answer:

$\frac{4}{5}$