1- A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.

Question

1- A 14-foot ladder is set up 4 feet from the base of a building. How far up the building does the ladder reach? Round your answer to the nearest tenth of a foot.

A. 13.4 feet
B. 14.6 feet<--
C. 16.5 feet
D. 18.0 feet

2- The library is 10 kilometers south of Aaron’s home. The school is 10 kilometers east of Aaron’s home. How many kilometers, to the nearest tenth of a kilometer, is the library from the school?

A. 10.2 kilometers<--
B. 12.0 kilometers
C. 14.1 kilometers
D. 20.0 kilometers

3- Alina is flying a kite. The kite string is fully extended and measures 100 feet in length. The kite is 45 feet east of Alina. Which equation can be used to find the height of the kite? How high is the kite? Select two answers.

A. 45^2 + b^2 = 100^2 <--
B.100=0.5(45)(b)
C. 4.4 feet <--
D. 89.3 feet

I require assistance, please?

Answer 1

The answers are

A. 13.4 feet

C. 14.1 kilometers

A and D

Answer 2

#1 and #2 are incorrect

#3 is correct

Did you make a sketch for #1 and #2 to use the Pythagorean Theorem correctly?

Answer 3

On number 3, I changed my answers to A and D

Answer 4

Of course! I'd be happy to help you with these questions.

1. To find out how far up the building the ladder reaches, we can 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, the ladder is the hypotenuse, and the ladder, base of the building, and the height of the building form a right triangle. The ladder is 14 feet long, and it is set up 4 feet from the base of the building. We need to find the height of the building, which is the other side of the triangle.

So, using the Pythagorean theorem, we can write the equation as follows:
14^2 = 4^2 + b^2

Simplifying:
196 = 16 + b^2
b^2 = 196 - 16
b^2 = 180
b = √180 ≈ 13.4

Therefore, the ladder reaches approximately 13.4 feet up the building. The answer is A. 13.4 feet.

2. To find the distance between the library and the school, we can use the Pythagorean theorem again. In this case, the library and the school are at right angles to Aaron's home, forming a right triangle.

The library is 10 kilometers south of Aaron's home, and the school is 10 kilometers east of Aaron's home. We need to find the distance between the library and the school, which is the hypotenuse of the right triangle.

So, using the Pythagorean theorem, we can write the equation as follows:
Distance^2 = (10)^2 + (10)^2

Simplifying:
Distance^2 = 100 + 100
Distance^2 = 200
Distance = √200 ≈ 14.1

Therefore, the library is approximately 14.1 kilometers from the school. The answer is C. 14.1 kilometers.

3. To find the height of the kite, we can use the Pythagorean theorem once again. In this case, the kite string is fully extended and forms the hypotenuse of a right triangle, with one side being the distance east of Alina, and the other side being the height of the kite.

The kite string is 100 feet long, and the kite is 45 feet east of Alina. We need to find the height of the kite, which is the other side of the right triangle.

So, using the Pythagorean theorem, we can write the equation as follows:
100^2 = 45^2 + b^2

Simplifying:
10000 = 2025 + b^2
b^2 = 10000 - 2025
b^2 = 7975
b = √7975 ≈ 89.3

Therefore, the height of the kite is approximately 89.3 feet. The equation that can be used to find the height of the kite is A. 45^2 + b^2 = 100^2, and the height is approximately 89.3 feet. The answer is A and D.

Answer 5

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