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Question

Two persons are standing on the opposite sides of a tower. They observe the angles of elevation of the top of the tower to be 30 and 38 respectively. Find the distance between them, if the height of the tower is 50 m. [2 MARKS]

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Solution

Diagram: 0.5 Mark
Concept: 0.5 Mark
Application: 1 Mark


Two persons A and B are standing on the opposite side of the tower TR and height of tower TR = 50 m and angles of elevation with A and B are 30 and 38 respectively. Let AR = x and RB = y.

Now in right ΔTAR

tan θ=TRARtan 30=50x

13=50x

x=503 m=86.60 m

Again in right ΔTRB,

tan 38=50yy tan 38=50

y=50tan 38=500.7813=63.99 or 64.00 m

Distance between A and B

=x+y=86.60+64.00=150.60m=150.6m

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