Question

A drone is flying at a height of 100 m above the ground. It observes on its right two stationary cars on a highway at angles of depression 45° and 30°. On the basis of above information, answer the following questions: Find the distance of each car from the point on the highway just below the drone.

Hint:

The tangent of an angle is the ratio of the opposite side (height of drone) to the adjacent side (distance from point below drone).

Answer 1

Step 1: Understand the geometry of the problem.
Let the height of the drone be 100 m. The angles of depression are given as 45° and 30° for the two cars. Using the tangent of the angles of depression, we can find the distance of each car from the point on the highway directly below the drone.
Step 2: Use the tangent formula for the first car.
For the first car, the angle of depression is 45°. The tangent of an angle is given by: \[ \tan(\theta) = \frac{\text{height}}{\text{distance}}. \] For the first car, \( \theta = 45^\circ \), and the height is 100 m. Thus, the distance \( x_1 \) of the first car from the point on the highway is: \[ \tan(45^\circ) = \frac{100}{x_1} \quad \Rightarrow \quad 1 = \frac{100}{x_1} \quad \Rightarrow \quad x_1 = 100 \, \text{m}. \]
Step 3: Use the tangent formula for the second car.
For the second car, the angle of depression is 30°. The distance \( x_2 \) of the second car from the point on the highway is: \[ \tan(30^\circ) = \frac{100}{x_2} \quad \Rightarrow \quad \frac{1}{\sqrt{3}} = \frac{100}{x_2} \quad \Rightarrow \quad x_2 = 100\sqrt{3} \, \text{m} \approx 173.21 \, \text{m}. \]