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: If the drone rises to 150 m, find the tangent of the angle of depression of each car at the new height.

Hint:

When the height of the drone changes, the tangent of the angle of depression changes according to the new height and distance.

Answer 1

Step 1: Recalculate the new distances using the new height.
For the first car, the height of the drone is now 150 m. The new distance \( x_1' \) is: \[ \tan(\theta_1') = \frac{150}{x_1'} \quad \Rightarrow \quad \tan(\theta_1') = \frac{150}{100} = 1.5. \] For the second car, the new distance \( x_2' \) is: \[ \tan(\theta_2') = \frac{150}{x_2'} \quad \Rightarrow \quad \tan(\theta_2') = \frac{150}{173.21} \approx 0.866. \] Thus, the new tangents of the angles of depression are: \[ \tan(\theta_1') = 1.5 \quad \text{and} \quad \tan(\theta_2') \approx 0.866. \]