Jaclynn is building a playhouse for her cats. She designs a ramp from one level to the other for them to climb. The ramp length is 4 feet, and the difference between the two levels is 2.5 feet. What is the approximate angle of elevation formed by the ramp? Round your answer to the nearest whole degree.
To find the angle of elevation formed by the ramp, we will use the tangent function.
The tangent function is defined as the ratio of the length opposite the angle to the length adjacent to the angle. In this case, the opposite side is the height difference of 2.5 feet and the adjacent side is the ramp length of 4 feet.
Therefore, the tangent of the angle of elevation is given by:
tan(Angle) = Opposite/Adjacent = 2.5/4 = 0.625
To find the angle, we can take the inverse tangent (arctan) of this value:
Angle = arctan(0.625) ≈ 31.3 degrees
Rounding to the nearest whole degree, the approximate angle of elevation formed by the ramp is 31 degrees.