pythagorean theorem

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Tags

CCSS.8.G.B.8

Front

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

Back

The formula to find the length of the hypotenuse (c) is: c = √(a² + b²).

Tags

CCSS.8.G.B.8

Front

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

Back

Using the Pythagorean Theorem: c = √(3² + 4²) = √(9 + 16) = √25 = 5.

Tags

CCSS.8.G.B.7

Front

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

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2. The side opposite the 30° angle is the shortest.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the length of the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

How do you find the distance between two points (x1, y1) and (x2, y2) in a coordinate plane?

Back

The distance can be found using the formula: d = √((x2 - x1)² + (y2 - y1)²).

Tags

CCSS.HSG.GPE.B.7

Front

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

Back

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

Tags

CCSS.8.G.B.8

Front

If a TV has a diagonal measurement of 40 inches and a height of 30 inches, how do you find the width?

Back

Use the Pythagorean Theorem: 30² + b² = 40². Solve for b to find the width.

Tags

CCSS.8.G.B.8

Front

What is the area of a right triangle with a base of 6 and a height of 8?

Back

Area = (1/2) * base * height = (1/2) * 6 * 8 = 24 square units.

Tags

CCSS.6.G.A.1

Front

What is the perimeter of a right triangle with sides 5, 12, and 13?

Back

Perimeter = 5 + 12 + 13 = 30 units.

Tags

CCSS.3.MD.D.8