Question

A fire truck parks 28 ft away from a building. The fire truck extends its ladder 65 ft. How far up the building from the trucks roof does the extension ladder reach?

Answer 1

To calculate the height the fire truck's ladder reaches up the building, we use the Pythagorean theorem and find that the ladder reaches approximately 58.66 ft up the building from the truck's roof.

Step-by-step explanation:

The question at hand involves using the Pythagorean theorem to calculate the height at which the fire truck's ladder reaches the building. The given values are the distance from the truck to the building (28 ft) and the length of the extended ladder (65 ft).

To find the height up the building that the ladder reaches, we assume a right triangle where the distance from the truck to the building is one leg, the height the ladder reaches is the other leg, and the ladder itself is the hypotenuse. We can set up the equation as follows:

1. Let x be the height up the building that the ladder reaches.
2. The Pythagorean theorem states that a2 + b2 = c2, where a and b are the legs, and c is the hypotenuse.
3. Substitute the given values to get the equation 282 + x2 = 652.
4. Solve for x by first calculating 282, which equals 784, then calculating 652, which equals 4225. Subtract 784 from 4225 to get 3441.
5. Find the square root of 3441 to get x ≈ 58.66 ft.

Therefore, the ladder reaches approximately 58.66 ft up the building from the truck's roof.