Question

can a 15 cm, 9 cm, and 12 cm be the sides of a right triangle

Answer 1

thanks

Answer 2

If a right triangle has side lengths of 8 and 15, how long is the hypotenuse?

Answer 3

Lane places his 30-foot ladder against a house he is painting. If the bottom of the ladder is 7 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?

Answer 4

Haley is standing in the base path between second and third base when she fields the ball. She is 24 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth. numbers used are 32 ft and 24 ft

Answer 5

Yes, a triangle with side lengths of 15 cm, 9 cm, and 12 cm can form a right triangle.

To check if it is a right triangle, 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 lengths of the other two sides.

Let's calculate:

15^2 = 225

9^2 + 12^2 = 81 + 144 = 225

Since both calculations result in 225, we can conclude that the triangle is a right triangle.

Answer 6

You're welcome! If you have any more questions, feel free to ask.

Answer 7

To find the length of the hypotenuse, you can use the Pythagorean theorem. According to the theorem, in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Let's calculate:

8^2 = 64

15^2 = 225

Now, add these two values together:

64 + 225 = 289

Finally, take the square root of 289 to find the length of the hypotenuse:

sqrt(289) = 17

Therefore, the length of the hypotenuse is 17 units.

Answer 8

In this scenario, we have a right triangle formed by the ladder, the ground, and the side of the house. The ladder acts as the hypotenuse, and we need to find the length of the other side, which is the height above the ground where the ladder touches the house.

Using the Pythagorean theorem, we can calculate this side:

a^2 + b^2 = c^2

Where:
a = 7 feet (distance from the base of the house to the bottom of the ladder)
c = 30 feet (length of the ladder, which is the hypotenuse)

Let's solve for b:

b^2 = c^2 - a^2

b^2 = 30^2 - 7^2

b^2 = 900 - 49

b^2 = 851

Now, take the square root of both sides:

b = sqrt(851)

b ≈ 29.2

Hence, the top of the ladder is approximately 29.2 feet above the ground where it touches the house.

Answer 9

To solve this problem, we can use the Pythagorean theorem. The distance between second base and first base is one side of a right triangle, and the distance between second base and third base is the other side. The throw Haley needs to make is the hypotenuse.

Using the given numbers, we can calculate the distance she needs to throw the ball:

a = 24 ft (distance between second base and third base)
b = 32 ft (distance between second base and first base)

Using the Pythagorean theorem:

c^2 = a^2 + b^2

c^2 = 24^2 + 32^2

c^2 = 576 + 1024

c^2 = 1600

Taking the square root of both sides, we find:

c = sqrt(1600)

c = 40

Therefore, Haley needs to throw the ball approximately 40 feet from second base to first base.