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.

To find the height of the pedestal, we can use trigonometry. Let's denote the height of the pedestal as "h".

From the given information, we know that the angle of elevation of the top of the statue is 60° and the angle of elevation of the top of the pedestal is 45°.

Step 1: Draw a diagram to visualize the situation. Label the statue's height as 1.6 m and the height of the pedestal as "h".

Step 2: From the diagram, we can see that we have a right triangle formed by the ground, the top of the pedestal, and the point where we are observing from. Let's call this triangle ABC, where A is the observer's position, B is the top of the pedestal, and C is the top of the statue.

Step 3: In triangle ABC, we have two angles: angle BAC (angle of elevation of the top of the statue) = 60° and angle BCA (angle of elevation of the top of the pedestal) = 45°.

Step 4: We can use the tangent function to find the height of the pedestal. The tangent of an angle is equal to the opposite side divided by the adjacent side.

In triangle ABC, the opposite side of angle BAC is the height of the statue (1.6 m) and the adjacent side is the height of the pedestal (h).

So, we have the equation: tan(60°) = 1.6 / h

Step 5: Solve the equation for h. We can rearrange the equation to isolate h:

h = 1.6 / tan(60°)

Step 6: Use a calculator to find the value of tan(60°) and calculate the height of the pedestal.

tan(60°) ≈ 1.732

h = 1.6 / 1.732

h ≈ 0.924 m

Therefore, the height of the pedestal is approximately 0.924 meters.