How long a ladder must you have to reach the top of a 15-foot wall if the bottom of the ladder is placed 4 feet from the base of the wall? Round to the nearest tenth of a foot.
14.5 ft
15.5 ft
17.0 ft
19.0 ft
To find the length of the ladder, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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, the height of the wall represents one side, and the distance of the ladder from the wall represents the other side.
Using the Pythagorean theorem, we have:
ladder^2 = height^2 + distance^2
ladder^2 = 15^2 + 4^2
ladder^2 = 225 + 16
ladder^2 = 241
ladder ≈ √241
ladder ≈ 15.5 ft
Therefore, the ladder must be approximately 15.5 feet long to reach the top of the 15-foot wall when the bottom is placed 4 feet from the base.
The rounded answer is 15.5 ft.
What is the length of the hypotenuse of the triangle?
Triangle A B C. Side A C is 7 feet and side C B is 4 feet. Hypotenuse A B is unknown.
StartRoot 22 EndRoot ft
StartRoot 33 EndRoot ft
StartRoot 57 EndRoot ft
StartRoot 65 EndRoot ft
To find the length of the hypotenuse, we can again use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, side AC and side CB are the two sides of the right triangle, and the hypotenuse AB is the unknown.
Using the Pythagorean theorem, we have:
AB^2 = AC^2 + CB^2
AB^2 = 7^2 + 4^2
AB^2 = 49 + 16
AB^2 = 65
AB ≈ √65
AB ≈ 8.06 ft
Therefore, the length of the hypotenuse AB is approximately 8.06 feet.
The rounded answer is StartRoot 65 EndRoot ft.
Which is a perfect square?
5
8
36
44
The perfect square among the given numbers is 36.
Joseph and Isabelle left Omyra’s house at the same time. Joseph jogged north at 8 kilometers per hour, while Isabelle rode her bike west at 12 kilometers per hour. Omyra tried to figure out how far apart they were after 1.5 hours. Her work is shown below. Which statements describe her errors? Check all that apply.
A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.
8 squared + 12 squared = d squared. 64 + 24 = d squared. 88 = d squared. StartRoot 88 EndRoot = d. 9.4 almost-equals d.
She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph’s distance and 18 km for Isabelle’s distance.
She did not square the 12 in the problem. She should have used 12 squared = 144.
She did not evaluate 8 squared correctly. She should have used 8 squared = 8 (2) = 16.
She did not evaluate StartRoot 88 EndRoot correctly. She should have used StartRoot 88 EndRoot almost-equals 44.
She should not have taken the square root of each side when solving. She should have just divided each side by 2.
She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
The incorrect statements made by Omyra are:
- She did not find the full distance each traveled in 1.5 hours. She should have used 12 km for Joseph's distance and 18 km for Isabelle's distance.
- She did not square the 12 in the problem. She should have used 12 squared = 144.
- She did not evaluate 8 squared correctly. She should have used 8 squared = 8 x 8 = 64.
- She did not evaluate √88 correctly. She should have used √88 ≈ 9.38.
- She should not have added the squares in the first step. She should have used 12 squared minus 8 squared = d squared.
Therefore, the correct statements are:
- She should not have taken the square root of each side when solving. She should have just divided each side by 2.
- A right triangle. The distance north from Omyra's House is 8 kilometers, and the distance west is 12 kilometers.
Which equation correctly shows how to determine the distance between the points (9, –2) and (6, 3) on a coordinate grid?
d = StartRoot (6 minus 3) squared + (9 minus (negative 2)) squared EndRoot
d = StartRoot (6 + 3) squared + (9 + (negative 2)) squared EndRoot
d = StartRoot (6 minus 9) squared + (3 minus (negative 2)) squared EndRoot
d = StartRoot (6 + 9) squared + (3 + (negative 2)) squared EndRoot
The correct equation to determine the distance between the points (9, -2) and (6, 3) on a coordinate grid is:
d = √((6 - 9)^2 + (3 - (-2))^2)
Simplifying the equation gives:
d = √((-3)^2 + (5)^2)
d = √(9 + 25)
d = √34
Therefore, the correct equation is:
d = √34
Each point on the edge of a circle is equidistant from the center of the circle. The center of a circle is located at (6, 3). Which point on the y-axis could be on the edge of the circle if the distance from the center of the circle to the edge is 10 units?
(0, –1)
(0, 1)
(0, 5)
(0, –5)