Question

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

Answer 1

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.