Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.