The ladder will reach 122 ft up the building.
The 120 feet of the extended ladder, since it will be leaning against the building, will be the hypotenuse of the right triangle. x will be the height from the top of the fire truck to the point where the ladder hits the building. 75° is the angle the ladder will make with the fire truck.
We have an angle, the side opposite the angle, and the hypotenuse. Opposite/hypotenuse is the ratio for sine, so we set up our equation as such:
x/120 = sin 75
Multiply both sides by 120:
120(x/120) = 120*sin 75
x = 120*sin 75
x ≈116
However, this is just from the top of the fire truck to the point where the ladder hits the building. We still add the 6 feet from the top of the truck to the ground. 116+6 = 122.
