Question

mackah is looking at a bird perched on top of a street light. her line of sight, which is the diagonal distance to the top of the street light, is 16 feet, and she is standing 8 feet from the base of the street light. use the inverse of cosine to find the angle of elevation with which she is looking at the bird. round your answer to the nearest whole degree. (1 point) 40 50 60 65

Explanation:

Step1: Recall cosine - ratio formula

In a right - triangle formed by the line of sight, the horizontal distance, and the vertical distance from the observer's horizontal level to the top of the street light, if the angle of elevation is $\theta$, the adjacent side to the angle $\theta$ is the horizontal distance $AB$ and the hypotenuse is the line of sight $AC$. The cosine of an angle in a right - triangle is given by $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, $AB = 8$ feet and $AC=16$ feet.

Step2: Calculate the cosine of the angle of elevation

$\cos\theta=\frac{AB}{AC}=\frac{8}{16}=0.5$

Step3: Find the angle of elevation using inverse cosine

We know that $\theta=\cos^{- 1}(0.5)$. Using a calculator, $\cos^{-1}(0.5) = 60^{\circ}$

Answer:

$60$