Your office window is a = 35 feet high. Looking out your window, you find that the top of a statue lines up exactly with the bottom of a building that is b = 650 horizontal feet from your office. You know the statue is c = 175 feet from the building. How tall is the statue?
To find the height of the statue, we can use similar triangles. Let's break down the problem and use the given information:
1. Given:
- Height of the office window (a) = 35 feet
- Horizontal distance from the office to the building (b) = 650 feet
- Distance from the building to the top of the statue (c) = 175 feet
2. We are looking for:
- The height of the statue (x)
3. Now, let's set up a proportion between the similar triangles formed by the office window, the building, and the statue:
- The height of the office window to the distance from the office to the building is the same as the height of the statue to the distance from the building to the statue.
This can be expressed as:
a / b = x / c
4. Plugging in the given values into the equation:
35 / 650 = x / 175
5. Solve the proportion for x:
Cross-multiply to get:
35 * 175 = x * 650
Simplify:
6125 = 650x
Divide both sides by 650 to isolate x:
x = 6125 / 650
Calculate the value:
x = 9.4231
6. The height of the statue is approximately 9.4231 feet.
45
If the statue's height is h, then using similar triangles (from the diagram you drew, right?):
h/c = a/b
Now just plug in your numbers and solve for h