Pythagorean Thm & Special Right Triangles

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.

Front

What type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem only applies to right triangles.

Front

In a 30-60-90 triangle, what is the ratio of the lengths of the sides?

Back

The ratio of the lengths of the sides in a 30-60-90 triangle is 1 : √3 : 2.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the length of the hypotenuse is √2 times the length of each leg.

Front

If one leg of a 30-60-90 triangle is 7, what is the length of the hypotenuse?

Back

The hypotenuse is 7 * 2 = 14.

Front

What is the length of the shorter leg in a 30-60-90 triangle if the longer leg is 7?

Back

The shorter leg is 7 / √3.

Front

What is the length of the diagonal of a square with side length 9?

Back

The length of the diagonal is 9√2.

Front

If the height of a right triangle is 6 feet and the base is 8 feet, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10 feet, calculated using the Pythagorean Theorem: √(6² + 8²) = √(36 + 64) = √100 = 10.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.

Front

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

Back

In a right triangle, one angle is 90 degrees, and the sum of the other two angles is 90 degrees.