From the top of a tower of unknown height metres

MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Trigonometry · Applications of Trigonometry

Problem

From the top of a tower of unknown height

H

metres, the angle of depression of a point

P

on the horizontal ground is

52^\circ

. A point

Q

lies on the same horizontal line as

P

and is

78\,\text{m}

closer to the foot of the tower than

P

. The angle of depression of

Q

70^\circ

. (i) Using a suitable sketch, label all the known and unknown quantities involved. (ii) Write two equations in

H

and the horizontal distance

x

(in metres) from the foot of the tower to point

Q

. (iii) Solve these equations to find

H

and

x

. Give each answer correct to the nearest metre.