Answer:
Explanation:
The ramp, its vertical elevation, and the ground make a right triangle, with the length of the ramp being the hypotenuse, the vertical elevation one leg, and the horizontal distance (ground) the other leg.
The angle of elevation of a ramp is related with the hypotenuse and the opposite leg by the trigonometric ratio named sine:
In this problem, the length of the ramp. i.e the straight line distance of the ramp, is the hypotenuse, the distance the door is off the ground (the height of the ramp) is the opposite leg, and the angle α is the angle of elevation of the ramp.
Then:
Thus, the ramp will have an angle of elevation of 4.1º and you conclude that the 35 feet long is enough because the angle is smaller than the limit of 4.8º.
a) Yes, 35 feet is enough for the straight line distance of the ramp to meet the requirements
b)The angle of elevation is 4.1º
Pythagorean theorem states that in the right angle triangle the hypotenuse square is equal the square of the sum of the other two sides.
The ramp, its vertical elevation, and the ground make a right triangle, with the length of the ramp being the hypotenuse, the vertical elevation one leg, and the horizontal distance (ground) on the other leg.
The angle of elevation of a ramp is related with the hypotenuse and the opposite leg by the trigonometric ratio named sine:
sine (α) = opposite leg / hypotenuse
In this problem, the length of the ramp. i.e the straight line distance of the ramp, is the hypotenuse, the distance the door is off the ground (the height of the ramp) is the opposite leg, and the angle α is the angle of elevation of the ramp.
Then:
sine (α) = opposite leg / hypotenuse
sine (α) = 2.5 feet / 35 feet ≈ 0.07142857
α = arcsine(0.07142857) = 4.1º.
Thus, the ramp will have an angle of elevation of 4.1º and you conclude that the 35 feet long is enough because the angle is smaller than the limit of 4.8º.
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