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A right circular cylindrical tower, height 'h' and radius 'r'

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A right circular cylindrical tower, height $^{'} h^{'}$ and radius $^{'} r^{'}$ , stands on the ground. Let 'p' be a point in the horizontal plane ground and ABC be the semi-circular edge of the top of the tower such that B is the point in it nearest to p. The angle of elevation of the points of the tower such that B is the point in it nearest to p. The angles of elevation of the points A and B are $4 5^{0}$ and $6 0^{0}$ respectively. show that $\frac{h}{r} = \frac{3 ( 1 + 3 )}{2}$

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A right circular cylindrical tower, height

^{'} h^{'}

and radius

^{'} r^{'}

, stands on the ground. Let 'p' be a point in the horizontal plane ground and ABC be the semi-circular edge of the top of the tower such that B is the point in it nearest to p. The angle of elevation of the points of the tower such that B is the point in it nearest to p. The angles of elevation of the points A and B are

4 5^{0}

and

6 0^{0}

respectively. show that

\frac{h}{r} = \frac{3 ( 1 + 3 )}{2}

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Text solutionVerified

Let PQ = x

In $Δ PQB$

$tan 6 0^{\circ} = \frac{h}{x}$

$3 = \frac{h}{x}$

$h = x 3___(1)$

In $Δ A PC,$

$tan 4 5^{\circ} = \frac{h}{x + r}$

$l = \frac{h}{x + r}$

$\Rightarrow x + r = h$

$\Rightarrow \frac{h}{3} + r = h$ by (1)

$\Rightarrow h (1 - \frac{1}{3}) = r$

$\Rightarrow h \frac{( 3 - 1 )}{3} = r$

$\Rightarrow \frac{h}{r} = \frac{3}{3 - 1}$

$\Rightarrow \frac{h}{r} = \frac{3}{3 - 1} \times \frac{3 + 1}{3 + 1}$

$\Rightarrow \frac{h}{r} = \frac{3 ( 3 + 1 )}{2}$

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Question Text	A right circular cylindrical tower, height $^{'} h^{'}$ and radius $^{'} r^{'}$ , stands on the ground. Let 'p' be a point in the horizontal plane ground and ABC be the semi-circular edge of the top of the tower such that B is the point in it nearest to p. The angle of elevation of the points of the tower such that B is the point in it nearest to p. The angles of elevation of the points A and B are $4 5^{0}$ and $6 0^{0}$ respectively. show that $\frac{h}{r} = \frac{3 ( 1 + 3 )}{2}$
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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