What is the length of the missing side if the hypotenuse is 50 and one leg is 30?

Using the Pythagorean Theorem: $$30^2 + b^2 = 50^2$$ , which simplifies to $$900 + b^2 = 2500$$ . Therefore, $$b^2 = 1600$$ , so $$b = 40$$ .

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

The Pythagorean Theorem is used in various fields such as architecture, construction, navigation, and physics to calculate distances and ensure structures are built correctly.

If a right triangle has a hypotenuse of 20 and one leg of 15, what is the length of the other leg?

Using the Pythagorean Theorem: $$15^2 + b^2 = 20^2$$ , which simplifies to $$225 + b^2 = 400$$ . Therefore, $$b^2 = 175$$ , so $$b = \text{sqrt}(175) \text{ or approximately } 13.2$$ .

What is the area of a right triangle with legs of lengths 3 and 4?

The area of a right triangle is given by the formula: $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$$ . Thus, $$\text{Area} = \frac{1}{2} \times 3 \times 4 = 6$$ .

What is the perimeter of a right triangle with legs of lengths 5 and 12?

First, find the hypotenuse using the Pythagorean Theorem: $$5^2 + 12^2 = c^2$$ , which gives $$c = 13$$ . The perimeter is then $$5 + 12 + 13 = 30$$ .

What is the distance between two points (3, 4) and (7, 1) in a coordinate plane?

Use the distance formula: $$d = \text{sqrt}((x_2 - x_1)^2 + (y_2 - y_1)^2)$$ . Thus, $$d = \text{sqrt}((7 - 3)^2 + (1 - 4)^2) = \text{sqrt}(16 + 9) = 5$$ .

What is the relationship between the angles in a right triangle?

In a right triangle, one angle is always 90 degrees, and the sum of the other two angles is always 90 degrees, making the total sum of angles equal to 180 degrees.

Unit 4 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

If one side of a right triangle is 6 and the other side is 8, what is the length of the hypotenuse?

Back

3.

FLASHCARD QUESTION

Front

What is the length of the missing side if one side is 5 and the hypotenuse is 13?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

If a right triangle has legs of lengths 9 and 12, what is the length of the hypotenuse?

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

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