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

Answer:

• 52.35 m

Step-by-step 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 = $\sqrt{x^2+y^2} =\sqrt{39.25^2+34.64^2} = 52.35m$

Note, all numbers are rounded