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The angle of elevation of the top of a tower from two point at

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The angle of elevation of the top of a tower from two point at a distance 4 cm and 9 cm from the base of the tower and in the same straight line with it are complementary. prove that the height of tower is 6 m.

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The angle of elevation of the top of a tower from two point at a distance 4 cm and 9 cm from the base of the tower and in the same straight line with it are complementary. prove that the height of tower is 6 m.

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Text solutionVerified

REF. Image.

Given :

AB = 9 cm

DB=4 cm

θ + ϕ = 9 0^{\circ}

To prove :

BC = 6 c m

proof :

△ A BC, ∠ B = 9 0^{\circ}

t an θ = \frac{h}{4}

[t an θ = \frac{p er p e n d i c u l a r}{ba se}]

... (1)

△ A BC, ∠ B = 9 0^{\circ}

t an ϕ = \frac{h}{9}

...(2)

t an (θ + ϕ) = \frac{t an θ + t an ϕ}{1 - t an θt an ϕ}

t an (90) = \frac{h /4 + h /9}{1 - t an θ t an ϕ}

[from (1) and (2)

t an 90 = \infty

so,

1 - t an θt an ϕ = 0

1 = t an θ t an ϕ

From (1) and (2)

\frac{h}{4} \times \frac{h}{9} = 1

h^{2} = 36

h = 6 c m

Hence, proved.

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Question Text	The angle of elevation of the top of a tower from two point at a distance 4 cm and 9 cm from the base of the tower and in the same straight line with it are complementary. prove that the height of tower is 6 m.
Answer Type	Text solution:1
Upvotes	150

The angle of elevation of the top of a tower from two point at a distance 4 cm and 9 cm from the base of the tower and in the same straight line with it are complementary. prove that the height of tower is 6 m.

Text solutionVerified

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