Question

1. yash looks downwards at a frisbee that has landed 4 m away from her feet. if yash eye level is 1.7 m above the ground, find the angle of depression. give your answer to 1 decimal place.

Explanation:

Step1: Find the vertical distance

The vertical distance from Yash's eye - level to the Frisbee is \(4 - 1.7=2.3\) m.

Step2: Use the tangent function

Let the angle of depression be \(\theta\). In the right - triangle formed, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). The opposite side to the angle of depression (which is equal to the angle of elevation from the Frisbee to Yash's eye - level) is \(4 - 1.7 = 2.3\) m and the adjacent side is \(4\) m. So, \(\tan\theta=\frac{2.3}{4}\).

Step3: Calculate the angle

\(\theta=\tan^{- 1}(\frac{2.3}{4})\). Using a calculator, \(\tan^{-1}(0.575)\approx30.0^{\circ}\)

Answer:

\(30.0^{\circ}\)