Q39. - Algebra 1

Question

Suppose a roller coaster climbs 208 feet higher than its starting point, moving horizontally 360 feet. When it comes down, it moves horizontally 44 feet.

a. How far will it travel to get to the top of the ride?

b. How far will it travel on the downhill track?

Step-by-Step Solution

Answer

a. Distance travelled by the roller coaster to get on top is 415.8 ft.

b. Distance travelled by the roller coaster on the downhill track is 212.6 ft.

Step 1. State the concept of Pythagoras Theorem.

The Pythagorean Theorem describes the relationships between the sides of a right triangle. The square of the hypotenuse, the side opposite the right angle, is equal to the sum of the squares of the two sides.

${\text{hypotenuse}}^2={\text{adjacent}}^2+{\text{opposite}}^2$

Step 2. Find the hypotenuse during uphill.

The hypotenuse during uphill can be calculated as follows:

$\begin{array}{c}{\text{hypotenuse}}^2={\text{adjacent}}^2+{\text{opposite}}^2\\ ={\left(360\right)}^2+{\left(208\right)}^2\\ =129600+43264\\ =172864\\ \text{hypotenuse}=\sqrt{172864}\\ =415.8\end{array}$

Step 3. Find the hypotenuse during downhill.

The hypotenuse during downhill can be calculated as follows:

$\begin{array}{c}{\text{hypotenuse}}^2={\text{adjacent}}^2+{\text{opposite}}^2\\ ={\left(44\right)}^2+{\left(208\right)}^2\\ =1936+43264\\ =45200\\ \text{hypotenuse}=\sqrt{45200}\\ =212.6\end{array}$

Step 4 . Write the conclusion.

Therefore, the distance travelled by the roller coaster to get on top is 415.8 ft. and Distance travelled by the roller coaster on the downhill track is 212.6 ft.