Algebra homework

Question

A 30 m ladder and 26 ladder we’re leaned against a building. The bottom of the longer ladder was 8m farther from the building than the bottom of the shorter ladder, but both ladders reached the same distance up the building. Find this distance.

A. 10m

B. 12m

C. 18m

D. 24m

Answer 1

construct 2 right triangles with same height, but base 8 m apart longer for the longer ladder = 30 m, shorter =26 m

height up the ladder = 24 m for both ladders

answer is D. 24 m

use trig or the Pythagorean theorem

30^2 = (x+8)^2 + h^2

26^2 = x^2 + h^2

x = 10

h = sqr(26^2 -100) = sqr576 = 24 m