MATH SOLVE

2 months ago

Q:
# A 70ft ladder is mounted 10ft above the ground on a fire truck. The bottom of the ladder is 40ft from the wall of a building.the top of the ladder is touching the building. How high off the ground is the top of the ladder

Accepted Solution

A:

Please refer to my attachments for visual guidelines.

We are going to solve your problem by using the pythagorean theorem, a^2+b^2 = c^2, where a and b are the legs of the triangle, and c is the hypotenuse (the longest side).

The length of the ladder is equal to 70ft (hypotenuse); one leg is the distance between the wall and the bottom of the ladder - 40 ft, the other leg is unknown for it is the distance between 10 ft above the ground and the top of the ladder-represented by "x". Using pythagorean theorem, a^2+b^=c^2, we have x^2+40^2 = 70^2. Solving the exponents, we have x^2 + 1600 = 4900.

Isolating the variable x, we have x^2 = 4900-1600. Futher simplying, x^2 = 3300. Thus, x = √3300 or 57.4456264654 ft.

Adding 10 ft to x, therefore, the top of the leadder is 67.4456264654 ft off the ground.

We are going to solve your problem by using the pythagorean theorem, a^2+b^2 = c^2, where a and b are the legs of the triangle, and c is the hypotenuse (the longest side).

The length of the ladder is equal to 70ft (hypotenuse); one leg is the distance between the wall and the bottom of the ladder - 40 ft, the other leg is unknown for it is the distance between 10 ft above the ground and the top of the ladder-represented by "x". Using pythagorean theorem, a^2+b^=c^2, we have x^2+40^2 = 70^2. Solving the exponents, we have x^2 + 1600 = 4900.

Isolating the variable x, we have x^2 = 4900-1600. Futher simplying, x^2 = 3300. Thus, x = √3300 or 57.4456264654 ft.

Adding 10 ft to x, therefore, the top of the leadder is 67.4456264654 ft off the ground.