Question

1. a playhouse includes a 15 - foot slide, and due to safety regulations, the base of the slide is 12 feet from the base of the playhouse structure. how tall is the top of the slide? a 1.7 feet b 3 feet c 9 feet d 19.2 feet (with a right triangle diagram labeled 15 feet (hypotenuse), 12 feet (one leg), x feet (the other leg))

Explanation:

Step1: Identify the triangle type

The slide, playhouse height, and base form a right triangle. Hypotenuse \( c = 15 \) ft, one leg \( a = 12 \) ft, find the other leg \( x \).

Step2: Apply Pythagorean theorem

Pythagorean theorem: \( a^2 + x^2 = c^2 \). Substitute values: \( 12^2 + x^2 = 15^2 \).

Step3: Solve for \( x^2 \)

Calculate \( 12^2 = 144 \), \( 15^2 = 225 \). So \( x^2 = 225 - 144 = 81 \).

Step4: Find \( x \)

Take square root: \( x = \sqrt{81} = 9 \) feet.

Answer:

C. 9 feet