A 10-foot ramp must make an angle of 30° with the ground if it is to reach a certain window. What angle must a 15-foot ramp make with the ground to reach the same window?

The problem above creates a right triangle as the ramp reaches a window making an angle from the ground.

Given:

Hypotenuse = 10 ft ramp

θ = 30°

Find:

Opposite side = O

θ = at 15 ft. ramp

First, we will find the height of the certain window. This is considered to be the opposite side and the ramp serves as the hypotenuse. We can use the SOH function in Pythagorean theorem

sin 30° = O / 10

O = 10 (sin 30°) ⇒ simplify to get the opposite side

O = 5 ft ⇒ height if the certain window from the ground

Use the obtained value to get the angle needed by a 15 ft ramp leaning on the same window.

sin θ = 5 / 15

sin θ = 1 / 3 ⇒ simplify further to get the angle

θ = arc sin (1/3)

θ = 19.47°