If the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

Using the Pythagorean Theorem: $$b = \text{sqrt}(10^2 - 6^2) = \text{sqrt}(100 - 36) = \text{sqrt}(64) = 8$$ .

What is the value of c if a = 8 and b = 15?

Using the Pythagorean Theorem: $$c = \text{sqrt}(8^2 + 15^2) = \text{sqrt}(64 + 225) = \text{sqrt}(289) = 17$$ .

If a right triangle has legs of lengths 7 and 24, what is the length of the hypotenuse?

Using the Pythagorean Theorem: $$c = \text{sqrt}(7^2 + 24^2) = \text{sqrt}(49 + 576) = \text{sqrt}(625) = 25$$ .

What is the Pythagorean triplet?

A Pythagorean triplet consists of three positive integers a, b, and c, such that $$a^2 + b^2 = c^2$$ . An example is (3, 4, 5).

If the lengths of the two legs of a right triangle are equal, what can be said about the triangle?

The triangle is an isosceles right triangle, where the angles opposite the equal sides are both 45 degrees.

What is the area of a right triangle with legs of lengths 6 and 8?

The area can be calculated using the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \times 8 = 24$$ .

How do you determine if a triangle is a right triangle using side lengths?

To determine if a triangle with sides a, b, and c is a right triangle, check if $$c^2 = a^2 + b^2$$ , where c is the longest side.

Pythagorean Theorem Flashcards

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14 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

What is the formula to find the length of the hypotenuse?

Back

3.

FLASHCARD QUESTION

Front

In a right triangle, which side is the hypotenuse?

Back

The hypotenuse is the side opposite the right angle and is always the longest side in a right triangle.

4.

FLASHCARD QUESTION

Front

If one side of a right triangle is 3 and the other is 4, what is the length of the hypotenuse?

Back

5.

FLASHCARD QUESTION

Front

True or False: The hypotenuse is always the longest side in a right triangle.

Back

True.

6.

FLASHCARD QUESTION

Front

If the lengths of the two legs of a right triangle are 5 and 12, what is the length of the hypotenuse?

Back

7.

FLASHCARD QUESTION

Front

What is the relationship between the sides of a right triangle?

Back

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