Question

An observer at the top of a tower of height 20m sees a man due East of him at an angle of depression of 27°. He sees another man due south of him at an angle of depression 30°. Find the distance between the men on the ground.

hint: question is from trigonometry. bearings.

Answer 1

• 52.35 m

Explanation:

Refer to picture.

Let the distance to men are x and y and the distance between them is d.

The angle of depreciation is 27° and 30°, hence top angle of the triangle is 63° or 60°.

Find the distance from the tower to men:

• x = 20 tan 63° = 39.25 m
• y = 20 tan 60° = 34.64 m

The distance between men is:

• d =
  `√(x^2+y^2) =√(39.25^2+34.64^2) = 52.35m`

Note, all numbers are rounded