Question

A woman of height 1.3m, standing on top of a building of height 28.7m, views another building across the field.She observes that the angle of depression of the bottom of the building 39 and the angle of depression of the top of the building is 21. Both building stand on level ground. a Calculate the distance the woman from is from the base of the building across the field measured along her line of sight. b Find the height of the building.

Answer 1

• line of sight: 47.7 m
• building height: 15.8 m

Explanation:

You want the distance along a woman's line of sight to the base of a building if she is 30 m above the ground and the angle of depression is 39°. You also want to know the height of that building if the angle of depression to its top is 21°.

Distance

The distance along the line of sight is the hypotenuse of a right triangle that has an angle of 39° opposite her height of 30 m. The sine relation is relevant:

Sin = Opposite/Hypotenuse

distance = (30 m)/sin(39°) ≈ 47.7 m

The distance along the line of sight is about 47.7 m.

Height

The height of the building can be found using the law of sines in triangle BGW shown in the attachment.

w/sin(W) = b/sin(B)

where W is the angle between the angles of depression, 39° -21° = 18°, b is the distance we just found, and B is the angle 90°+21° at the top of the building. Then w, the height of the building, is ...

w = b·sin(W)/sin(B) = (47.67 m)·sin(18°)/sin(111°) ≈ 15.8 m

The height of the building is about 15.8 m.

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