ICSE Class X Math 2015 Solved Paper

Question : 40

Total: 52

The horizontal distance between two towers is 120m. The angle of elevation of the top and angle of depression of the bottom of the first tower as observed from the second tower is 30∘ and 24∘ respectively.

Find the height of the two towers. Give your answer correct to 3 significant figures.

Solution:

Let AB and CD are two towers.

BD=120m=EC,∠ACE=30∘,∠CBD=24∘‌. ‌
In right angle △CBD ,
tan‌24∘‌=‌

=‌

120

CD‌=120×0.4452
‌=53.42m.
In right angle △ACE ,
tan‌30∘‌=‌

=‌

120

AE‌=120×0.5773
‌=69.28m
AB‌=AE+EB
‌=AE+CD‌‌[EB=CD]
‌=69.28+53.42
‌=122.70m.
Height of 1st tower is 122.70m and 2nd tower is 53.42m.

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