A tower stands on level ground

MATHEMATICS · Subjective · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

A tower stands on level ground. From point

A

, the angle of elevation of the top of the tower is

\alpha

(where

45^\circ < \alpha < 90^\circ

). After moving

60\,\text{m}

directly away from the tower to point

B

, the angle of elevation becomes

(90^\circ - \alpha)

. (a) Taking the height of the tower to be

h\,\text{m}

and the initial horizontal distance

AB_0

between point

A

and the foot of the tower to be

d\,\text{m}

, write two separate equations in

h

and

d

using the given angles. (b) Eliminate

d

to derive a single formula expressing

h

in terms of

\alpha

only. (c) Using the formula obtained in part (b), calculate the height of the tower when

\alpha = 60^\circ

(give your answer correct to two decimal places).