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A statue, 1.6 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.

Answer :

Final answer:

The height of the pedestal, given the angles of elevation and the height of the statue, can be computed using the principles of trigonometry. The pedestal height is approximately 0.74m.

Explanation:

This is essentially a trigonometry problem involving right triangles. Here, we are given the angles of elevation to the top of the statue and the top of the pedestal and the height of the statue. Hence, we can solve this using the tangent of the angles of elevation.

Let the height of the pedestal be h1. Then the total height is h1 + 1.6. We can construct a right triangle with the line of sight to the top of the statue, the line from the top of the pedestal directly down to the observation point, and the line from the observation point to the top of the statue. The tangent of the angle 60 is then (h1 + 1.6) / d, where d is the distance from the observation point to the base of the pedestal. The tangent of the angle 45 is h1 / d. Because the tangents of these two angles are equal to each other, we can set these two equations equal to each other and solve for h1, the height of the pedestal:

Tan 60 = (h1 + 1.6) / d

Tan 45 = h1 / d

By setting these two equations equal to each other and solving for h1, we get that h1 = 1.6(√3 - 1), which is approximately 0.74m.

Learn more about Trigonometry here:

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