1.75-metre tall man, standing at the foot of a tower, sees the top of a hill 40 metres away at an elevation of 60°.

Question

A 1.75-metre tall man, standing at the foot of a tower, sees the top of a hill 40 metres away at an elevation of 60°. Climbing to the top of the tower, he sees it at an elevation of 50°. Calculate the heights of the tower and the hill.

Answer 1

In the right triangle CEF

BD = CE = AF = HG = 40m

tan 60 = \(\frac{EF}{CE}\)

EF = 40 x tan 60

= 40 x 1.732

= 17.32 x 4

= 69.28 m

AB = tower

DF = hill

Height of hill = 69.28 + 1.75 = 71.03 m In the right triangle HGF,

tan 50 = \(\frac{GF}{HG}=\frac{GF}{40}\)

GF = 40 × tan 50= 40 × 1.1918 = 47.67 m 

Height of tower = 71.03 – (47.67 + 1.75) 

= 71.03 – 49.42 = 21.61 m