Given the right triangle below, use the sine function to write a trigonometric expression for the missing angle $\(\theta\)$.

• A. $\(\theta\)=\(\sin\)^{-1}\(\left\)(\(\frac{5}{13}\]\right\))$
• B. $\(\theta\)=\(\sin\)^{-1}\(\left\)(\(\frac{12}{13}\]\right\))$
• C. $\(\theta\)=\(\sin\)^{-1}\(\left\)(\(\frac{5}{12}\]\right\))$
• D. $\(\theta\)=\(\sin\)^{-1}\(\left\)(\(\frac{13}{12}\]\right\))$

Answer: (A)

Verified step by step guidance

1. Identify the sides of the right triangle: the hypotenuse is 13, the opposite side to angle θ is 5, and the adjacent side is 12.
2. Recall the definition of the sine function in a right triangle: sin(θ) = opposite/hypotenuse.
3. Substitute the known values into the sine function: sin(θ) = 5/13.
4. To find the angle θ, use the inverse sine function: θ = sin⁻¹(5/13).
5. This expression, θ = sin⁻¹(5/13), represents the measure of the angle θ in terms of the sine function.