Question

62º, 28º

What is the relationship of the sides in this triangle based on the Pythagorean Theorem?
m^2 + n^2 = __

Answer 1

[AI-generated answer — Bot GPT 3.5]

m² + n² = c², where c is the length of the hypotenuse.

Answer 2

Apply the Pythagorean Theorem to decide whether a triangle with side lengths 16 mm, 30 mm, and 32 mm is a right triangle.

A. It is a right triangle because 16^2 + 30^2 = 1,156.
B. It is not a right triangle because 16^2 + 30^2 ≠ 32^2.
C. It is not a right triangle because 16 + 30 ≠ 32.
D. It is a right triangle because 16 + 30 = 46.

Answer 3

[AI-generated answer — Bot GPT 3.5]

B. It is not a right triangle because 16^2 + 30^2 ≠ 32^2.

Answer 4

If a triangle has sides of length 12 and 16, how long is the hypotenuse?

Answer 5

[AI-generated answer — Bot GPT 3.5]

To find the length of the hypotenuse of a right triangle using the Pythagorean Theorem, we use the formula:

a² + b² = c²

where a and b are the lengths of the two legs of the triangle, and c is the length of the hypotenuse.

In this case, a = 12 and b = 16. Plugging these values into the formula, we get:

12² + 16² = c²

144 + 256 = c²

400 = c²

Taking the square root of both sides, we have:

c = √400

c = 20

Therefore, the length of the hypotenuse is 20 units.

Answer 6

30 ft., 90 ft.

A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 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.
__ feet

Answer 7

[AI-generated answer — Bot GPT 3.5]

To find the distance the shortstop needs to throw the ball, we can use the Pythagorean Theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).

In this case, the distance from the shortstop to second base (a) is 30 ft and the distance from second base to first base (b) is 90 ft.

Using the Pythagorean Theorem, we have:

c² = a² + b²

c² = 30² + 90²

c² = 900 + 8100

c² = 9000

Taking the square root of both sides:

c = √9000

c ≈ 94.8683 ft

Rounding to the nearest tenth, the shortstop needs to throw the ball approximately 94.9 feet.

Answer 8

What Pythagorean triple is generated by multiplying each integer in the Pythagorean triple (20, 21, 29) by 5?

(__,__,145)

Answer 9

[AI-generated answer — Bot GPT 3.5]

By multiplying each integer in the Pythagorean triple (20, 21, 29) by 5, we get:

(20*5, 21*5, 29*5) = (100, 105, 145)

Therefore, the Pythagorean triple generated is (100, 105, 145).

Answer 10

(3, 2) , (7, 8)

Apply the Pythagorean Theorem to find the length between the two points. Round your answer to the nearest hundredth.

Answer 11

[AI-generated answer — Bot GPT 3.5]

To find the length between the two points (3, 2) and (7, 8), we can use the distance formula, which is derived from the Pythagorean theorem.

The formula to find the distance between two points (x1, y1) and (x2, y2) is:

d = √((x2 - x1)² + (y2 - y1)²)

In this case, (x1, y1) = (3, 2) and (x2, y2) = (7, 8).

Using the formula, we have:

d = √((7 - 3)² + (8 - 2)²)
= √(4² + 6²)
= √(16 + 36)
= √52
≈ 7.21

Rounding to the nearest hundredth, the length between the two points is approximately 7.21.