Answer:
To find the angle that the replacement ramp makes with the horizontal, we can use the concept of trigonometry. Specifically, we can use the tangent function, which relates the angle of inclination to the length of the opposite side (vertical) and the adjacent side (horizontal).
Let's first find the tangent of the given angle of 16° using a scientific calculator:
tan(16°) ≈ 0.2867
Now, we can set up a proportion to find the angle (let's call it θ) for the replacement ramp:
(29 ft) / (40 ft) = (vertical length) / (horizontal length)
Simplifying the proportion:
29 / 40 = (vertical length) / 40
To find the vertical length, we can multiply the tangent of the given angle by the horizontal length:
(vertical length) = (40 ft) * (0.2867) ≈ 11.468 ft
Now, we can set up a new proportion to find the angle θ for the replacement ramp:
(vertical length) / (40 ft) = tan(θ)
Substituting the values we found:
11.468 ft / 40 ft = tan(θ)
To isolate the angle θ, we can take the inverse tangent (also known as arctan or tan^(-1)) of both sides:
θ = arctan(11.468 ft / 40 ft)
Using a scientific calculator, we find:
θ ≈ 16.17°
Therefore, the replacement ramp makes an angle of approximately 16.17° with the horizontal.
Step-by-step explanation:
