A roller coaster is being built with a very steep drop and falls 64 feet over a horizontal distance of 160 ft.
a. What is the percentage grade of this drop? Round to the nearest tenth of a percent.
I did 64/160 = .4 so as a percentage that is 40%
b. What will the actual length of the track be in this section? Round to the nearest tenth of a foot.
I used the pythagorean theorem so 64^2 + 160^2 = c^2 then took the square root of that and got 172.3 feet
looks good
a. To find the percentage grade of the drop, you correctly divided the vertical drop (64 feet) by the horizontal distance (160 feet). The formula for finding the percentage grade is (vertical drop / horizontal distance) * 100.
So, in this case, (64 / 160) * 100 = 0.4 * 100 = 40%. Therefore, the percentage grade of the drop is 40%, which is correct.
b. To find the actual length of the track in this section, you correctly used the Pythagorean theorem. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the vertical drop is one side (64 feet) and the horizontal distance is the other side (160 feet). Let's call the length of the track in this section "c". So the equation becomes:
64^2 + 160^2 = c^2
Simplifying this equation, we have:
4096 + 25600 = c^2
29696 = c^2
Now, to find the value of "c" (the length of the track), we take the square root of both sides of the equation:
√29696 = √c^2
c ≈ √29696
c ≈ 172.3 feet (rounded to the nearest tenth)
Therefore, the actual length of the track in this section is approximately 172.3 feet, which is correct.