A wheelchair ramp is said to have an angle of 4.5° with the ground. the deck at the top of the ramp is 20 inches above ground level.
a) how long should the ramp be? round your answer to the nearest tenth of an inch.
c) how far from the deck should the ramp begin? Round your answer to the nearest tenth of an inch.
length: 20/x = sin 4.5°
distance: 20/x = tan 4.5°
To find the length of the wheelchair ramp, we can use trigonometry. The angle of 4.5° forms a right triangle with the ramp, where the height from the ground to the deck is the vertical leg and the length of the ramp is the hypotenuse.
a) To find the length of the ramp, we can use the following formula:
ramp length = height / sin(angle)
In this case, the height is 20 inches and the angle is 4.5°. Let's substitute these values into the formula:
ramp length = 20 / sin(4.5°)
Using a calculator, we find:
ramp length ≈ 262.7 inches
Rounding to the nearest tenth of an inch, the length of the ramp should be approximately 262.7 inches.
c) To find the distance from the deck where the ramp should begin, we can use trigonometry again. This time, we are interested in the horizontal leg of the right triangle, which represents the distance from the deck to the start of the ramp.
We can use the following formula:
horizontal distance = ramp length * cos(angle)
Using the previously calculated ramp length of 262.7 inches and the angle of 4.5°, let's substitute these values into the formula:
horizontal distance = 262.7 * cos(4.5°)
Again, using a calculator, we find:
horizontal distance ≈ 261.5 inches
Rounding to the nearest tenth of an inch, the ramp should begin approximately 261.5 inches from the deck.