Given a right triangle with sides $a$, $b$, and hypotenuse $c$, and angle $\angle lkj$ opposite side $a$, which equation can be used to find the measure of angle $\angle lkj$?

• A. $\angle lkj=arcsin\left(\frac{b}{c}\right)$
• B. $\angle lkj=arcsin\left(\frac{a}{c}\right)$
• C. $\angle lkj=arctan\left(\frac{a}{b}\right)$
• D. $\angle lkj=arccos\left(\frac{a}{c}\right)$

Answer: (B)

Verified step by step guidance

1. Identify the sides relative to the angle \( \angle lkj \): the side opposite the angle is \( a \), the adjacent side is \( b \), and the hypotenuse is \( c \).
2. Recall the definition of the sine function in a right triangle: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \).
3. Since \( \angle lkj \) is opposite side \( a \), the sine of this angle is \( \sin(\angle lkj) = \frac{a}{c} \).
4. To find the measure of the angle \( \angle lkj \), use the inverse sine (arcsin) function: \( \angle lkj = \arcsin\left(\frac{a}{c}\right) \).
5. Verify that the other options do not correctly represent the relationship for this angle: arcsin(\( \frac{b}{c} \)) uses the adjacent side, arctan(\( \frac{a}{b} \)) uses opposite over adjacent, and arccos(\( \frac{a}{c} \)) uses cosine which is adjacent over hypotenuse.