Question

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

Explanation:

Step1: Identify sides relative to $x$

In right $\triangle LJK$, right-angled at $L$:

• Hypotenuse: $JK = 15$ in
• Opposite to $\angle x$: $LK$
• Adjacent to $\angle x$: $LJ = 10$ in

Step2: Recall cosine definition

Cosine of an angle in a right triangle is $\frac{\text{Adjacent}}{\text{Hypotenuse}}$.

Step3: Substitute values

$\cos(x) = \frac{\text{Adjacent to } x}{\text{Hypotenuse}} = \frac{10}{15}$

Answer:

$\cos(x) = \frac{10}{15}$ (the third option)