Question

which equation can be used to find the measure of angle ljk?
○ sin(x) = 10/15
○ sin(x) = 15/10
○ cos(x) = 10/15
○ cos(x) = 15/10

Explanation:

Step1: Recall sine - cosine definitions

In a right - triangle, for an acute angle \(x\), \(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}\) and \(\cos(x)=\frac{\text{adjacent}}{\text{hypotenuse}}\).

Step2: Identify opposite and adjacent sides

Assume the right - triangle has an angle \(x = \angle LJK\). If the side opposite to \(\angle LJK\) has length \(10\) inches and the hypotenuse has length \(15\) inches.

Step3: Apply the sine formula

By the definition of sine, \(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}=\frac{10}{15}\).

Answer:

\(\sin(x)=\frac{10}{15}\)