What is the value of $$y$$ if $$y^2 = 128$$ ?

To find $$y$$ , take the square root: $$y = \text{sqrt}(128) = 8\text{sqrt}(2)$$ .

What is the height of a cone with a radius of 5 cm and a slant height of 13 cm?

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

What is the formula for the distance between two points in a coordinate plane?

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

If $$x^2 + 36 = 100$$ , what is $$x$$ ?

Rearranging gives $$x^2 = 64$$ , so $$x = \text{sqrt}(64) = 8$$ or $$x = -8$$ .

What is the definition of a right triangle?

A right triangle is a triangle that has one angle measuring 90 degrees.

How do you calculate the length of the hypotenuse if both legs are equal?

If both legs (a) of a right triangle are equal, the hypotenuse (c) can be calculated as: $$c = a\text{sqrt}(2)$$ .

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

The Pythagorean Theorem is used in various real-life applications such as construction, navigation, and physics to determine distances and angles.

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

The perimeter (P) of a right triangle is the sum of the lengths of all three sides: $$P = a + b + c$$ .

Chapter 7.1 Pythagorean Theorem 2023-2024 Flashcards

Student preview

15 questions

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1.

FLASHCARD QUESTION

Front

What is the Pythagorean Theorem?

Back

2.

FLASHCARD QUESTION

Front

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side in a right triangle, use the Pythagorean Theorem: if you know the lengths of two sides, you can rearrange the formula to solve for the missing side.

3.

FLASHCARD QUESTION

Front

If one side of a right triangle is 14 and the other is 48, what is the length of the hypotenuse?

Back

4.

FLASHCARD QUESTION

Front

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

Back

5.

FLASHCARD QUESTION

Front

What is the height of a ramp if it is 21 feet long and 19 feet away from the building?

Back

6.

FLASHCARD QUESTION

Front

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

Back

7.

FLASHCARD QUESTION

Front

How do you express a side length in simplest radical form?

Back

To express a side length in simplest radical form, factor the number under the square root into its prime factors and simplify by taking out pairs.

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