Question

what is the measure of the angle labeled a in the scale drawing of the dog pen? a $sin^{-1}(\frac{8}{13})$ b $cos^{-1}(\frac{8}{13})$ c $\tan^{-1}(\frac{8}{13})$ d $\tan^{-1}(\frac{13}{8})$

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Identify opposite and adjacent sides for angle A

For angle $A$ in the right - triangle formed, assume the vertical side is the opposite side and the horizontal side is the adjacent side. Let the length of the opposite side be $8$ and the length of the adjacent side be $4$.

Step3: Determine the inverse - tangent formula for the angle

We know that $\theta = \tan^{- 1}(\frac{\text{opposite}}{\text{adjacent}})$. Substituting the values of opposite and adjacent sides, we get $\theta=\tan^{-1}(\frac{8}{4})$.

Answer:

D. $\tan^{-1}(2)$