Solving Trigonometric Equations in Context Practice Test

A drone camera measures an angle of depression $\theta$ from the horizontal to a target on level ground. The drone is 120 m above the ground, and the horizontal distance from the point directly below the drone to the target is 160 m. The model is $$\tan(\theta)=\frac{120}{160}.$$ Which angle solves the model within the given interval $0^\circ<\theta<90^\circ$?

A pendulum’s horizontal displacement from center is modeled by $$x(\theta)=0.8\sin(\theta)$$ (meters), where $\theta$ is the phase angle. During one cycle, $0\le \theta\le 2\pi$. At what angle(s) is the displacement $x=0.4$ m?

Solve: $0.8\sin(\theta)=0.4$.