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A man standing at a point P is watching the top of a tower, wh

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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of $3 0^{\circ}$ .The man walks some distance towards the tower and then his angle of elevation of the top of the tower is $6 0^{\circ}$ . If the height of the tower is 30 m, then the distance he moves is:

22 m

223 m

20 m

203 m

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A man standing at a point P is watching the top of a tower, which makes an angle of elevation of

3 0^{\circ}

.The man walks some distance towards the tower and then his angle of elevation of the top of the tower is

6 0^{\circ}

. If the height of the tower is 30 m, then the distance he moves is:

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Text solutionVerified

△ A PC

, In

△ PBC

tan 3 0^{o} = \frac{30}{x + y}

tan 6 0^{o} = \frac{30}{y}

\frac{1}{3} = \frac{30}{x + y}

3 = \frac{30}{y}

∴ x + y = 303

∴ y = \frac{30}{3}

∴ x + \frac{30}{3} = 303

∴ x = 303 - \frac{30}{3} = \frac{30 \times 3 - 30}{3} = \frac{90 - 30}{3} = \frac{60}{3} \times \frac{3}{3}

∴ x = \frac{60 3}{3}

∴ x = 203 m

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Question Text	A man standing at a point P is watching the top of a tower, which makes an angle of elevation of $3 0^{\circ}$ .The man walks some distance towards the tower and then his angle of elevation of the top of the tower is $6 0^{\circ}$ . If the height of the tower is 30 m, then the distance he moves is:
Answer Type	Text solution:1
Upvotes	150