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 80 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 20°. How far away from the building is the sculpture? Round your answer to the nearest hundredth.

tan20=80/x

(x)tan20=80
(x)(0.3639702343)=80
x=219.80

To find the distance from the building to the sculpture, we can use the tangent function.

Let's call the distance from the building to the sculpture "x".

In the given situation, the angle of depression is the angle formed between the line of sight from the top of Nisha's window to the bottom of the sculpture and the horizontal line.

The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the opposite side is the vertical distance from the top of the window to the ground (80 feet) and the adjacent side is the horizontal distance from the window to the sculpture (x).

So we have:

tan(20°) = opposite/adjacent
tan(20°) = 80/x

To solve for x, we can rearrange the equation:

x = 80 / tan(20°)

Using a calculator, we find:

x ≈ 227.06

Therefore, the sculpture is approximately 227.06 feet away from the building. Rounded to the nearest hundredth, the distance is 227.06 feet.

To find the distance from the building to the sculpture, we can use the trigonometric ratio tangent (tan) since we know the angle of depression.

Let's call the distance from the building to the sculpture "x".

We can set up the equation:
tan(20°) = (height of the window) / x

Plugging in the known values:
tan(20°) = 80 / x

To find "x", we need to isolate it. We can start by multiplying both sides of the equation by "x":
x * tan(20°) = 80

Now, divide both sides of the equation by tan(20°) to solve for "x":
x = 80 / tan(20°)

Using a calculator, let's evaluate this expression:
x ≈ 229.18

Rounding to the nearest hundredth, the sculpture is approximately 229.18 feet away from the building.

Tan20 = 80/x.

X =