We are tasked to solved for the length of the ramp having an inclination of 15 degrees with the ground and 10 feet from the end of the ramp to the base of the building of the ground. Using trigonometric properties, we have a formula given an angle and the its opposite sides which is,
sin(Angle)=opposite/hypothenuse
hypothenuse would be the distance or the length of the ramp.
so we have,
sin(15)=10/hypothenuse
Cross-multiply, we have,
hypothenuse=10/sin(15)
using scientific calculator having a DEG mode,
hypothenuse=38.63703
Rounding of in nearest tenth we get,
hypothenuse=38.6 ft
Therefore, the ramp is 38.6 ft long