Question

A vertical tower is 20 m high from the horizontal ground. The angle of depression of aball from the top of the tower is 42°. Calculate the distance, in m, of the ball from thebase of the tower

Answer 1

22.2 m

Step-by-step explanation

Let us make a sketch of the problem.

From the diagram:

T = top of the tower

B = Ball

O = Base of the tower

Now, we have to find x, which is the distance from the ball to the base of the tower.

Since the angle of depression is 42°, it means that angle

To find x, we can apply Pythagoras Rule:

`\begin{gathered} \tan (<\text{OTB) = }(x)/(20) \\ \Rightarrow\text{ x = 20 }\cdot\text{ tan(48)} \\ x\text{ = 20 }\cdot\text{ 1.11} \\ x\text{ = 22.2 m} \end{gathered}`

The distance of the ball from the base of the tower is 22.2 m