Question

A 6-foot ladder touches the side of a building at a point 5 feet above the ground. At what height would a 18-foot ladder touch the building if it makes the same angle with the ground as the shorter ladder?

Answer 1

Answer:

15 feet above the ground

Step-by-step explanation:

We know sinθ = opposite/hypotenuse where h = height of the ladder above the ground = opposite = 5ft and L = length of ladder = hypotenuse side = 6 feet. sinθ = h/L

For the new ladder to make the same angle, sinθ must be the same, so let h' = height of new ladder above the ground and L' = length of new ladder = 18 ft

sinθ = h'/L'

So. h'/L' = h/L

h' = hL'/L

substituting the values of the variables, we have

h' = 5 ft × 18 ft/6 ft

= 5 ft × 3

= 15 ft

So, the 18-foot ladder must be placed 15 feet above the ground to make the same angle as the smaller ladder.