Nicholas places his 30-foot ladder against a house he is painting. If the foot of the ladder is 8 feet from the base of the house, how high above the ground is the top of the ladder touching the house, to the nearest tenth of a foot?(1 point)

Question

Responses

27.8 ft.
27.8 ft.

22.0 ft.
22.0 ft.

31.0 ft.
31.0 ft.

28.9 ft.

Answer 1

The ladder, the distance from the ladder's base to the house, and the height of the ladder touching the house form a right triangle. We can use the Pythagorean theorem to solve for the height of the ladder.

Let h represent the height of the ladder touching the house.

Using the Pythagorean theorem, we have:

(8^2) + (h^2) = (30^2)

64 + h^2 = 900

h^2 = 900 - 64

h^2 = 836

h = √836

h ≈ 28.9 ft

Therefore, the top of the ladder is approximately 28.9 feet above the ground when it touches the house. So the correct answer is 28.9 ft.

Answer 2

Which of the following statements is true?(1 point)
Responses

913
is an irrational number
9 over 13 is an irrational number

3.6¯¯¯
is equal to 113
3 point repeating 6 is equal to 11 thirds

44−−√
is a rational number
square root of 44 is a rational number

19−−√
is equal to 4.358

Answer 3

The correct statement is:

19√ is equal to 4.358.

This is because the square root of 19 is approximately 4.358.