Question

A 13-foot ladder is leaning against a house. If the base of the ladder is 5 feet away from the house, and it forms a right angle with the ground, what is the height of the ladder?

a) 12 feet
b) 10 feet
c) 8 feet
d) 15 feet

Answer 1

Using the Pythagorean theorem for the
`13-foot` ladder leaning against the house with its base
`5 feet` away we calculate the ladder's height above the ground to be
`12 feet`.

Step-by-step explanation:

To solve this problem, we apply the Pythagorean theorem because the ladder, the wall of the house, and the ground create a right triangle. The Pythagorean theorem states that in a right triangle, the square of the hypothenuse (c) is equal to the sum of the squares of the other two sides (a and b). The length of the ladder represents the hypothenuse, while the distance of the ladder base from the house represents one side of the triangle.

The formula of the Pythagorean theorem is:
`a² + b² = c²`. Given that the base of the ladder (a) is 5 feet away from the house and the length of the ladder (c) is 13 feet, we can calculate the height of the ladder above the ground (b) as follows:

• 
  `a² = 5² = 25`
• 
  `c² = 13² = 169`
• 
  `b² = c² - a² = 169 - 25 = 144`
• 
  `b = √144 = 12`

Therefore, the height of the ladder above the ground is
`12 feet`.