Question

which equation can be used to find the measure of angle ljk? \\(\bigcirc\\) \\(\sin(x) = \frac{10}{15}\\) \\(\bigcirc\\) \\(\sin(x) = \frac{15}{10}\\) \\(\bigcirc\\) \\(\cos(x) = \frac{10}{15}\\) \\(\bigcirc\\) \\(\cos(x) = \frac{15}{10}\\)

Explanation:

Step1: Identify sides relative to $x$

In right $\triangle KLJ$, $\angle L=90^\circ$. For $\angle J=x$:

• Opposite side: $KL$ (length unknown, not needed)
• Adjacent side: $LJ = 10$ in
• Hypotenuse: $KJ = 15$ in

Step2: Apply cosine definition

Cosine of an angle in a right triangle is $\frac{\text{Adjacent}}{\text{Hypotenuse}}$.
$\cos(x) = \frac{10}{15}$

Answer:

$\boldsymbol{\cos(x) = \frac{10}{15}}$ (Option: $\boldsymbol{\cos(x) = \frac{10}{15}}$)