Q. 84.1( 21 Votes )

# A statue 1.46 m tall, stands on the top of a pedestal. From a point on the ground, the angle of elevation of the top of the statue is 60° and from the same point, the angle of elevation of the top of the pedestal is 45° Find the height of the pedestal. [√3 = 1.73.]

Answer :

In the figure, let AB be the statue of height 1.46 m, BC the pedestal. Let D be a point on the ground from which the angles of elevation of the top of the statue and the top of the pedestal are 60° and 45° respectively. We are to find the height of the pedestal, which is BC. Join C and D. We get two triangles ACD and BCD with right angle at C. To find BC, we use trigonometric ratios to find the expression of CD from ACD and BCD and then equate them. Now, ∠BDC = 45°, ∠ADC = 60°, AB = 1.46 m.

From ∆ADC,

or,

Again, from ∆BCD,

or,

BC = CD

or,

or,

or,

or,

or,

Hence the answer is 2m.

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PREVIOUSA vertical tower stands on a horizontal plane and is surmounted by a vertical flagstaff of height 6 m. At a point on the plane, the angle of elevation of the bottom of the flagstaff is 30° and that of the top of the flagstaff is 60°. Find the height of the tower. [Use √3 = 1 .732.]NEXTThe angle of elevation of the top of an unfinished tower at a distance of 75 m from its base is 30°. How much higher must the tower be raised so that the angle of elevation of its top at the same point may be 60°? [Take √3 = 1.732.]

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