Question 19

Explanation

Problem Identification

We have a situation where a sniper is at a certain height shooting at a target below. We need to find the tangent of the angle of depression ($\tan \alpha$).

Determining Effective Height (Opposite Side)

The building height is $61.73$ meters. The target height is $173$ cm. We need to convert units first.

The height difference between the sniper (assumed at the top of the building) and the target's head is:

This is the opposite side ($opposite$) for the angle of elevation (which is equal to the angle of depression).

Determining Horizontal Distance (Adjacent Side)

The horizontal distance from the base of the building to the target is known to be $180$ meters. This is the adjacent side ($adjacent$).

Calculating Tangent of Angle of Depression

The angle of depression ($\alpha$) has a tangent value equal to the ratio of the opposite side to the adjacent side in the formed right-angled triangle.

Simplify the fraction:

Thus, the tangent value of the angle of depression is $\frac{1}{3}$.