Question

in the diagram of right triangle jkl below, $overline{kj} parallel overline{mn}$. which of the following ratios is equivalent to $cos m$?
answer
$\bigcirc \frac{jl}{jk}$
$\bigcirc \frac{jl}{kl}$
$\bigcirc \frac{jk}{jl}$
$\bigcirc \frac{jk}{kl}$

Explanation:

Step1: Identify parallel angle relationship

Since $\overline{KJ} \parallel \overline{MN}$, $\angle M = \angle K$ (corresponding angles). So $\cos M = \cos K$.

Step2: Apply cosine definition to $\angle K$

In right $\triangle JKL$, $\cos K = \frac{\text{adjacent side to } \angle K}{\text{hypotenuse}} = \frac{JK}{KL}$.

Answer:

$\boldsymbol{\frac{JK}{KL}}$ (Option: $\boldsymbol{\frac{JK}{KL}}$)