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Question
The length of the shadow of a statue increases by 8m, when the latitude of the sun changes from 45° to 30°. Calculate the height of the tower.
Solution
Let the height of the statue (AB) be h.
In ΔABC,
`tan45^circ = "AB"/"BC"`
⇒ BC = h
In ΔABD,
`tan30^circ = "AB"/"BD"`
`1/sqrt(3) = "AB"/("BC + CD")`
h + 8 = `sqrt(3)`h (∵ BC = h)
⇒ `"h"(sqrt(3)` - 1) = 8
⇒ h = `8/(sqrt(3) - 1) × (sqrt(3) + 1)/(sqrt(3) + 1)`
⇒ h = `(8(sqrt(3) + 1))/2 = 4(sqrt(3) + 1) = 4 xx 2.732 = 10.928 ≈ 10.93`
Thus, the height of the tower is 10. 93 m.
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