Question 6.6.9: Finding the Rotation Angle for a Security Camera A security ...
Finding the Rotation Angle for a Security Camera
A security camera is to be installed 20 feet away from the center of a jewelry counter. The counter is 30 feet long. What angle, to the nearest degree, should the camera rotate through so that it scans the entire counter? See Figure 87.
The counter center C, the camera A, and a counter end B form a right triangle. The angle at vertex A is \frac{\theta}{2}, \text { where } \theta is the angle through which the camera rotates. Note that
\begin{aligned}\tan \frac{\theta}{2} &=\frac{15}{20}=\frac{3}{4} & \\\frac{\theta}{2} &=\tan ^{-1} \frac{3}{4} \approx 36.87^{\circ} & \text { Use a calculator in Degree mode. } \\\theta & \approx 73.74^{\circ} & \text { Multiply both sides by } 2\end{aligned}
Set the camera to rotate through 74° to scan the entire counter.