Question

Nicolas places his 30 ft ladder against his house he is painting. If the foot of the ladder is 8 ft from the base of the house, how high above the ground is the top of the ladder touching the house. Nearest tenth.

Pythagorean’s Theorem

Answer 1

The top of the ladder is approximately 29.0 feet above the ground.

Step-by-step explanation:

To find the height above the ground that the top of the ladder is touching the house, we can use the Pythagorean Theorem. The theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the ladder represents the hypotenuse and the distance between the base of the ladder and the house represents one of the sides. Let's call the height of the ladder 'h'. We can set up the equation: h^2 = 30^2 - 8^2. Solving for 'h', we get h ≈ 29.0 feet.

Therefore, the top of the ladder is approximately 29.0 feet above the ground.

Answer 2

28.9'

Step-by-step explanation:

Using the Pythagorean Theorem:

Let a = 8' base

Let b = x

Let c = 30' ladder

a^2 X b^2 = c^2

(8)^2 X (x)^2 = (30)^2

64 X (x)^2 = 900 (Subtract 64 from both sides of the equation)

x^2 = 836

`√(x)  = √(836)`

x = 28.9'