Answer :
The height of the pedestal is approximately 0.6761 meters (or about 67.61 centimeters).
Let's call the height of the pedestal "h" meters. We already know the height of the statue is 1.6 meters. We have two angles of elevation, one for the top of the statue and one for the top of the pedestal, with the same point on the ground as the reference. We can use trigonometric relationships to solve for the height of the pedestal.
The angle of elevation to the top of the statue is given as 60 degrees.
This gives us the following trigonometric relationship:
tan(60°) = height of statue/distance from the point to the base of the statue.
tan(60°) = 1.6 / d, where d is the distance from the point to the base of the statue.
The angle of elevation to the top of the pedestal is 45 degrees.
This gives us another trigonometric relationship:
tan(45°) = (height of statue + height of pedestal) / distance from the point to the base of the pedestal.
tan(45°) = (1.6 + h) / d.
We now have a system of two equations with two unknowns:
1. tan(60°) = 1.6 / d
2. tan(45°) = (1.6 + h) / d
First, let's solve equation 1 for d:
d = 1.6 / tan(60°)
d ≈ 1.6 / 1.7321
d ≈ 0.9239 meters
Now, we substitute this value of d into equation 2:
tan(45°) = (1.6 + h) / 0.9239
Now, solve for h:
1 = (1.6 + h) / 0.9239
1 * 0.9239 = 1.6 + h
0.9239 = 1.6 + h
Subtract 1.6 from both sides to isolate h:
h = 0.9239 - 1.6
h ≈ -0.6761 meters
Since height cannot be negative, we discard the negative value. The height of the pedestal is approximately 0.6761 meters (or about 67.61 centimeters).
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