Question

A 70-ft ladder is mounted 10 ft above the ground on a fire truck. The bottom of the ladder is 40

ft 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?
about 67.4 ft
about 41.2 ft
about 34.8 ft
about 90.6 ft

Answer 1

`\text{Hello there!}\\\\\text{Use the Pythagorean theorem first:}\\\\a^2+b^2=c^2\\\\\text{Plug 70 to c since it's your hypotenuse and plug 40 to a}\\\\40^2+b^2=70^2\\\\\text{Solve for b:}\\\\40^2+b^2=70^2\\\\1600+b^2=4900\\\\\text{Subtract 1600 from both sides}\\\\b^2=3300\\\\\text{Square root}\\\\b=57.4456\\\\\text{Round to the nearest tenth}\\\\57.4\\\\\text{Add 10 to 55.4 because the ladder is 10 ft off the ground}\\\\67.4\\\\\boxed{\text{Answer: about 67.4 ft}}`