For a ramp with an angle of elevation of 14° and a height of 2.5 feet, how long is the horizontal distance of the ramp? Round your answer to the nearest tenth.
The horizontal distance of the ramp can be found using the trigonometric function tangent.
Let x be the length of the horizontal distance of the ramp.
Since the tangent of an angle is equal to the opposite side divided by the adjacent side, in this case it is:
tan(14°) = 2.5 ft / x
To solve for x, we can rearrange the equation:
x = 2.5 ft / tan(14°)
Using a calculator, the tangent of 14° is approximately 0.2493.
x = 2.5 ft / 0.2493 ≈ 10.03 ft
Therefore, the horizontal distance of the ramp is approximately 10.03 feet.