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in Trigonometry by (44.3k points)

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. [Use √3=1.73]

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Best answer

Draw a figure based on given instructions:

Where SP = Statue

PB = Pedestal

Angles of elevation of S and P are 60° and 45° respectively.

Let AB = x, PB = h

(units are in meters)

From figure:

Right △ABS:

tan 60° = SB/AB

√3 = SB/AB

√3 = (h + 1.46)/x …(1)

Again, from right △PAB:

tan 45° = PB/AB

1 = PB/AB = h/x

h = x …(2)

Equation (1) implies

√3 = (h + 1.46)/h (using equation (2))

h = 1.46/(√3 – 1)

= 1.46/(√3 – 1) x (√3 + 1)/(√3 + 1)

= 1.46/2 x (√3 + 1)

= 2

Height of the pedestal is 2 meters.

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