Shawn is about to ride a straight water slide. The launching platform is at the top of a tower that is 48 feet tall. The splash pool at the end of the slide is 36 feet from the base of the tower. How long is the water slide itself?
Question
Shawn is about to ride a straight water slide. The launching platform is at the top of a tower that is 48 feet tall. The splash pool at the end of the slide is 36 feet from the base of the tower. How long is the water slide itself?
Solution
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be written as: a² + b² = c².
In this case, the height of the tower is one side of the triangle (a), the distance from the base of the tower to the splash pool is the other side (b), and the length of the water slide is the hypotenuse (c).
Given: a = 48 feet (height of the tower) b = 36 feet (distance from the base of the tower to the splash pool)
We need to find c (length of the water slide).
Step 1: Square the lengths of the two sides: a² = 48² = 2304 b² = 36² = 1296
Step 2: Add these two values together: a² + b² = 2304 + 1296 = 3600
Step 3: Take the square root of this sum to find the length of the hypotenuse: c = √3600 = 60 feet
So, the water slide is 60 feet long.
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