Angle of Depression - Trigonometry

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.

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Solution Preview

...m T to F is 32.7 degrees, FTB is 57.3 degrees. cos(57.3)=27/TF, TF = 49.98 -->approx 50m.
(ii) Now, we are in a non-right triangle. We use the law of sines. Since the angle of depression of T to P is 22.6 degrees, so we know PTF is 10.1 degrees. sin(TPF)/50 = sin(10.1)/27.5, sin(TPF) = ...