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The angle of elevation of the top of a tower from two horizontal points (in opposite sides) at distances of 25 metre and 64 metre from the base of tower are x and 90° – x respectively. The height of the tower will be
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- 39 metre
- 89 metre
- 1.6 metre
- 40 metre
Correct Option: D
Let AB = Height of tower = h metre
BC = 25 metre
BD = 64 metre
∠ACB = x° and ∠ADB = (90 – x)
In ∆ABC,
| tan x = | BC |
| ⇒ tan x = | 25 |
In ∆ABD,
| tan (90° – x) = | BD |
| ⇒ cot x = | 64 |
| ∴ tanx . cotx = | × | 25 | 64 |
⇒ h² = 25 × 64
∴ h = √25 × 64 = 5 × 8
= 40 metre
