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Question 108
When the Sun ray’s inclination increases from $$30^\circ$$ to $$60^\circ$$, the length of the shadow of a tower decreases by 60 m. Find the height of the tower.
Solution
Assume the height of the tower = x and the shadow formed when the inclination = 60 is y.
In the given figure, tan60= $$\ \frac{\ x}{y}$$...............(1)
tan30=$$\ \frac{\ x}{y+60}$$...................(2)
Dividing 1 by 2, we get, $$\ \frac{\ y}{y+60}$$ = 3
=> y=30 =>x=y$$\sqrt{\ 3}$$ = 30$$\times\ $$1.732=51.96 m
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