Question

Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 60 feet from the ground.The angle of depression from the top of Nisha's window to the bottom of the sculpture is 25°. How far away from the building is the sculpture? Round youranswer to the nearest hundredth.

Answer 1

To find the distance from Nisha's apartment building to the sculpture, we can use trigonometry. The approximate distance is 139.56 feet.

Step-by-step explanation:

To find the distance from Nisha's apartment building to the sculpture, we can use trigonometry. Let's denote the distance from the building to the sculpture as 'x'. We have a right triangle formed by the height of the window (60 feet), the distance from the building to the sculpture ('x'), and the angle of depression (25°).

Using the trigonometric ratio for tangent, we can write:

tan(25°) = 60 / x

Now, we can solve for 'x' by isolating it on one side of the equation:

x = 60 / tan(25°)

Using a calculator, we can evaluate this expression to find the approximate value of 'x'. Rounding to the nearest hundredth, we have:

x ≈ 139.56 feet