Answer:
AB ≈ 1.8 ft . . . . . ramp height
BC ≈ 29.9 ft . . . distance along the ground
Explanation:
a)
The 30-ft length in the diagram is the hypotenuse of the right triangle. The vertical height of interest is the side of the triangle opposite the given angle. That means the relevant trig relation is ...
Sin = Opposite/Hypotenuse
sin(3.5°) = AB/(30 ft)
Multiplying by 30 ft gives ...
AB = (30 ft)sin(3.5°) ≈ 1.831 ft
AB ≈ 1.8 ft
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b)
The distance along the ground is the side adjacent to the angle, so the relevant trig relation is ...
Cos = Adjacent/Hypotenuse
BC = (30 ft)cos(3.5°) ≈ 29.944 ft
BC ≈ 29.9 ft