Given a right triangle with an angle $\theta$ and an adjacent side of length $a$, and hypotenuse of length $c$, which equation finds the value of $\theta$?

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

Answer: (A)

Verified step by step guidance

1. Identify the sides of the right triangle relative to the angle \( \theta \): the adjacent side is \( a \), and the hypotenuse is \( c \).
2. Recall the definition of the cosine function in a right triangle: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \).
3. Set up the equation using the given sides: \( \cos(\theta) = \frac{a}{c} \).
4. To find \( \theta \), apply the inverse cosine (arccos) function to both sides: \( \theta = \arccos\left(\frac{a}{c}\right) \).
5. This equation expresses \( \theta \) in terms of the known side lengths \( a \) and \( c \), allowing you to calculate the angle.