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Angle of depression

The foot, F, of a hill and the base B, of a vertical tower TB, 27 metres tall, are on the same horizontal plane. From the top, T, of the tower, the angle of depression of F is 32.7 degrees. P is a point on the hill 27.5 metres away from F along the line of greatest slope. T, B, F and P all lie in the same vertical plane. The angle of depression of P from T is 22.6 degrees.

a) Draw a sketch to represent the information given above

b) Show that: (i) TF is 50m approximately
(ii) sin TPF = 7/22 approximately

c) Calculate: (i)the gradient of the hill
(ii) the height, in metres, of P above F , giving your answer correct to the nearest metre.

Note: I am a CXC maths home tutor. For some reason the most efficient method and for soem parts the correct one seem to be eluding me. Needless to say this is both frustrating and embarrassing. Class is today at 4:30pm. It is now 8:11am here. Please help. Thanks.

Solution Preview

The key to this question is realizing that the situation is physically impossible unless the foot of the hill F is actually the foot on the far side of the hill!
a) see attached document
b) (i) To find TF, we simply use the properties of cosine in a right triangle. Since the angle of depression ...

Solution Summary

This shows how to sketch a situation and find the angle of depression.