Question

Nick wants to build a banister for the staircase in his home. The height of the staircase is 8 feet, and the horizontal distance from the bottom to the top of the staircase is 15 feet.

What is the length of the banister? Round to the nearest tenth, if necessary.

Answer 1

The length of the banister that Nick wants to build for his staircase, calculated using the Pythagorean theorem, is 17 feet.

Step-by-step explanation:

To calculate the length of the banister that Nick wants to build for the staircase, we can use the Pythagorean theorem which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, the height of the staircase (8 feet) and the horizontal distance (15 feet) are the two sides of a right triangle, and the banister will be the hypotenuse. The formula is:

c² = a² + b²

Where:

• a = 8 feet (height of the staircase)
• b = 15 feet (horizontal distance from the bottom to the top of the staircase)
• c = length of the banister (unknown)

Plugging in the values:

c² = 8² + 15²

c² = 64 + 225

c² = 289

Now, taking the square root of both sides to solve for c:

c = √289

c = 17 feet

Therefore, the length of the banister will be 17 feet.

Answer 2

Step-by-step explanation:

By the Pythagorean Theorem

c^2=a^2+b^2 ( where c is the hypotenuse and a and b are the legs of a right triangle)

c^2=15^2+8^2

c^2=225+64

c^2=289

c=17 feet