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°