Question

A man 1.5 metres tall standing on top of a mountain 298.5m high observes the angles of depressions of two flying boats D and C to be 28 and 34 degrees respectively. Calculate the distance between the boats.
Pls I need urgent answer plss

Answer 1

Answer:

119.45 meters

Step-by-step explanation:

This question can be solved using one of the three trigonometric ratios. The height mentioned is 298.5 + 1.5 = 300 m and the angle of depression is 28 degrees for Boat D and 34 degrees for Boat C. It can be seen that the required distance is given by x feet, which is the distance between the two boats. This forms two right angled triangle, as it can be seen in the diagram. The perpendicular is given by 300 m, the base is the unknown, and the angles 28 degrees for boat A and 34 degrees for boat B is is given, as shown in the attached diagram. Therefore, the formula to be used is:

tan θ = Perpendicular/Base (For the distance between the mountain and Boat D)

Plugging in the values give:

tan 28 degrees = 300/d.

d = 300/tan 28.

d = 564.22 m (to the nearest hundredth).

tan θ = Perpendicular/Base (For the distance between the mountain and Boat C)

Plugging in the values give:

tan 34 degrees = 300/c.

c = 300/tan 34.

c = 444.77 m (to the nearest hundredth).

The difference between d and c will be x, i.e. that distance between the boats. So 564.22 - 444.77 = 119.45 meters (to the nearest hundredth).

Therefore, the boats are 119.45 meters apart from each other!!!