Practice Test 6

A rotating spotlight points along the ground and then turns upward. The distance from the light to a wall is 25 m (horizontal), and the spot hits the wall at a height of 15 m. Let $\theta$ be the angle the beam makes with the ground. Which angle solves the model within the interval $0^\circ<\theta<90^\circ$?

Solve: $\tan(\theta)=\dfrac{15}{25}$.

A lighthouse beam makes an angle of depression $\theta$ from the horizontal to a boat. The lighthouse light is 48 m above sea level, and the boat is 90 m horizontally from the point directly below the light. Which angle represents the correct solution within $0^\circ<\theta<90^\circ$?

Solve: $\tan(\theta)=\dfrac{48}{90}$.