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)
Responses
27.8 ft.
27.8 ft.
22.0 ft.
22.0 ft.
31.0 ft.
31.0 ft.
28.9 ft.
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.
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
The correct statement is:
19√ is equal to 4.358.
This is because the square root of 19 is approximately 4.358.