What is the relationship between the sides of a 45-45-90 triangle?

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is $$\text{sqrt}(2)$$ times the length of a leg.

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

Using the Pythagorean Theorem: $$c = \text{sqrt}(5^2 + 12^2) = \text{sqrt}(25 + 144) = \text{sqrt}(169) = 13$$ .

What is the Pythagorean triple for the sides 8, 15, and ?

The missing side is 17, as $$8^2 + 15^2 = 17^2$$ .

How do you find the area of a right triangle?

The area of a right triangle is given by the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ .

What is the distance formula derived from the Pythagorean Theorem?

The distance between two points (x1, y1) and (x2, y2) is given by: $$d = \text{sqrt}((x2 - x1)^2 + (y2 - y1)^2)$$ .

What is the significance of the hypotenuse in a right triangle?

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

If the hypotenuse is 13 and one leg is 5, how do you find the other leg?

Set up the equation: $$5^2 + b^2 = 13^2$$ , then solve for b.

What is the Pythagorean Theorem used for in real life?

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.

Pythagorean Theorem Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

3.

FLASHCARD QUESTION

Front

What is the formula to find the length of the hypotenuse in a right triangle?

Back

4.

FLASHCARD QUESTION

Front

What is the opposite of squaring a number?

Back

The opposite of squaring a number is finding the square root.

5.

FLASHCARD QUESTION

Front

If a right triangle has sides of length 3 and 4, what is the length of the hypotenuse?

Back

6.

FLASHCARD QUESTION

Front

In a right triangle, if one side is 6 and the hypotenuse is 10, how do you find the other side?

Back

7.

FLASHCARD QUESTION

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

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