Question

a helicopter flies 665 feet above ground. what is the measure of the angle of depression from the helicopter to the girl’s line of sight? round to the nearest degree. 23° 25° 65° 67° (image shows a right triangle - related diagram with helicopter, girl, 665 ft height, 5 ft girl height, 280 ft horizontal distance)

Explanation:

Step1: Find the vertical distance

The helicopter is 665 feet above ground, and the girl is 5 feet tall. So the vertical distance from the helicopter to the girl's line of sight is $665 - 5 = 660$ feet. The horizontal distance is 280 feet.

Step2: Use the tangent function

We can use the tangent of the angle of depression (let's call it $\theta$). In the right triangle, $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}=\frac{660}{280}$.

Step3: Calculate the angle

First, calculate $\frac{660}{280}\approx2.3571$. Then, $\theta = \arctan(2.3571)$. Using a calculator, $\arctan(2.3571)\approx67^\circ$.

Answer:

67°