Question

The angles of elevation of the top of a tower from two points at a distance of 16 m and 8 m from the base of the tower and in the same straight line with it are complementary. Prove that the height of the tower is 12.
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Answer 1

Answer:

Hi your answer is as follows

Step-by-step explanation:

figure given below

x + y = 90 ----------- (given)

x = 90 - y --------- (1)

In triangle ABC,

$tan x = \frac{AB}{8} \\\\tan (90-y)=\frac{AB}{8} ~------------~(from~1)\\\\cot y = \frac{AB}{8}\\\\\frac{1}{tany} =\frac{AB}{8} \\\\\ tan(y) = \frac{8}{AB} ---------------------~(2)$

In triangle ABD,

$tan (y) = \frac{AB}{16} ~---------------~(3)\\\\Equating~2~and~3;$

$\frac{8}{AB} =\frac{AB}{16} \\\\AB^2 = 16 *8\\\\AB^2 = 128\\\\AB = \sqrt{128}\\\\AB = 11.37\\\\ AB = 12~cm ~ ( ~approx)$

Hence proved

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Hope it helps,

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