Q. 34.4( 29 Votes )

# An observer 1.5 m tall is 30 m away from a chimney. The angle of elevation of the top of the chimney from his eye is 60°. Find the height of the chimney.

Answer :

In the figure, let BD be the height of the man, i.e. BD = 1.5m. Let AE be the chimney in the figure. Join B and C. We get a triangle which is right angled at C. Clearly, BD = CE. Also, given that ∠ ABC = 60°. We use the trigonometric ratio tan which uses AC as height and BC as a base to find the height of the chimney AE.

Now, clearly CE = 1.5m. The height of the chimney is AE.

From ∆ABC,

or,

Thus, AC = 51.96m and CE = 1.5m. The height of the chimney

AE = AC + CE = 51.96 + 1.5 = 53.46 m.

Hence, the answer is 53.46 m.

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PREVIOUSA kite is flying at a height of 75 m from the level ground, attached to a string inclined at 60° to the horizontal. Find the length of the string, assuming that there is no slack in it. [Take √3 = 1.732.]NEXTThe angles of elevation of the top of a tower from two points at distances of 5 meters and 20 meters from the base of the tower and in the same straight line with it are complementary. Find the height of the tower.

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