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.]
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.