Question

fall 2025 geometry b wwva
right triangle relationships and trigonometry
which equation can be used to find the measure of angle ljk?
\\( \cos ( x ) = \frac { 10 } { 15 } \\)
\\( \sin ( x ) = \frac { 10 } { 15 } \\)
\\( \cos ( x ) = \frac { 15 } { 10 } \\)
\\( \sin ( x ) = \frac { 15 } { 10 } \\)

Explanation:

Step1: Recall trigonometric ratios

In a right - triangle, \(\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}\) and \(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}\).
For angle \(x = \angle LJK\), the adjacent side to angle \(x\) is \(10\) inches and the hypotenuse is \(15\) inches.

Step2: Apply the cosine formula

Using the formula \(\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}\), we substitute the values.
So, \(\cos(x)=\frac{10}{15}\)

Answer:

\(\cos(x)=\frac{10}{15}\) (the first option in the left - hand side of the given choices)