SOLUTION: Hi. In math class we are doing word problems with right triangles. Here is the problem: Suppose a roller coaster's height is 105 feet off the ground. The distance on the ground fro

Algebra ->  Triangles -> SOLUTION: Hi. In math class we are doing word problems with right triangles. Here is the problem: Suppose a roller coaster's height is 105 feet off the ground. The distance on the ground fro      Log On


   

Question 179555: Hi. In math class we are doing word problems with right triangles. Here is the problem: Suppose a roller coaster's height is 105 feet off the ground. The distance on the ground from the start of the hill to the top of the hill is 200 feet. How fat do you actually travel on the roller coaster's track?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
It would help you if you were to draw a diagram of the situation in which the right triangle's height represents the height of the roller coaster (105 ft.) and the triangle's base represents the roller coaster's distance from the start of the hill to the top of the hill (200ft.).
To answer the question "How far do you actually travel on the roller coaster's track?", you need to find the length of the hypotenuse of the right triangle. This can be done using the Pythagorean theorem: c%5E2+=+a%5E2%2Bb%5E2 where c is the hypotenuse and a and b are the lengths of the other two legs. So...
c%5E2+=+a%5E2%2Bb%5E2 Substitute a = 200ft. and b = 105ft.
c%5E2+=+%28200%29%5E2%2B%28105%29%5E2
c%5E2+=+40000%2B11025
c%5E2+=+51025 Take the square root of both sides of the equation.
c+=+sqrt%2851025%29 Using your calculator, you get...
highlight%28c+=+225.887%29 Rounding to the nearest foot, you get...
c = 226 feet as the distance actually traveled on the roller coaster's track.