What is the value of $$c$$ if $$a = 5$$ and $$b = 12$$ ?

Using the Pythagorean Theorem: $$c^2 = 5^2 + 12^2$$ , which simplifies to $$c^2 = 25 + 144$$ , so $$c^2 = 169$$ . Therefore, $$c = 13$$ .

In the equation $$a^2 + b^2 = c^2$$ , what do the variables represent?

In the equation, $$a$$ and $$b$$ represent the lengths of the legs of the right triangle, while $$c$$ represents the length of the hypotenuse.

If a triangle has sides of lengths 8, 15, and 17, is it a right triangle?

Yes, it is a right triangle because $$8^2 + 15^2 = 17^2$$ (64 + 225 = 289).

What is the first step to solve for a missing leg in a right triangle?

Identify the lengths of the hypotenuse and the other leg, then use the Pythagorean Theorem to set up the equation.

If the hypotenuse is 13 and one leg is 5, what is the length of the other leg?

Using the formula: $$b^2 = c^2 - a^2$$ , we have $$b^2 = 13^2 - 5^2$$ , which simplifies to $$b^2 = 169 - 25$$ , so $$b^2 = 144$$ . Therefore, $$b = 12$$ .

What is the significance of the Pythagorean Theorem in real life?

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

Can the Pythagorean Theorem be used for non-right triangles?

No, the Pythagorean Theorem only applies to right triangles. For non-right triangles, other methods such as the Law of Cosines are used.

What is the formula for the area of a right triangle?

The area of a right triangle can be calculated using the formula: $$Area = \frac{1}{2} \times a \times b$$ , where $$a$$ and $$b$$ are the lengths of the legs.

Pythagorean Theorem (Solving for the missing leg) 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 are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as 'a' and 'b' in the Pythagorean Theorem.

3.

FLASHCARD QUESTION

Front

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

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

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

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

What does it mean if a triangle is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees. The side opposite this angle is the hypotenuse.

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