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.