what angle does the ladder form with the ground?

Question

. An 18-foot ladder is leaning against the wall. If the ladder reaches a height of 9 feet on the wall, what angle does the ladder form with the ground?

Answer 1

The ladder, and thus the hypotenuse of the triangle formed, is 18 ft. The height that the ladder reaches on the wall is 9 ft. This is the side opposite the angle that the ladder forms with the ground.

Since we have the opposite side (O) and the hypotenuse (H), we can look at (SOH)(CAH)(TOA) to tell us which trigonometric ratio we need to consider. We can clearly see we need to use sine, because we have O and H. Now,

sin(θ) = O/H

Inverting the sine function,

θ = sin^-1(O/H)

We can substitute our given values and solve by looking up or remembering common trig ratios.

θ = sin^-1(9/18)

θ = sin^-1(1/2)

θ = 30°, or π/6 radians