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: c² = a² + b².

Front

What are the special right triangles?

Back

The two special right triangles are the 45-45-90 triangle and the 30-60-90 triangle. In a 45-45-90 triangle, the legs are equal, and the hypotenuse is √2 times the length of a leg. In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

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

Back

To find the length of the hypotenuse, use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the lengths of the other two sides.

Front

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

Back

To find the length of a leg, rearrange the Pythagorean Theorem: a = √(c² - b²) or b = √(c² - a²), depending on which leg you are solving for.

Front

What is the ratio of the sides in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30-degree angle, √3 is the length of the side opposite the 60-degree angle, and 2 is the length of the hypotenuse.

Front

What is the length of the hypotenuse in a 45-45-90 triangle with legs of length 10?

Back

The length of the hypotenuse is 10√2.

Front

If one leg of a 30-60-90 triangle is 5, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 10.

Front

What is the length of the leg opposite the 60-degree angle in a 30-60-90 triangle if the hypotenuse is 12?

Back

The length of the leg opposite the 60-degree angle is 6√3.

Front

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

Back

To determine if a triangle is a right triangle, check if a² + b² = c² holds true for the lengths of the sides.

Front

What is the area of a right triangle with legs of length 6 and 8?

Back

The area is 24 square units, calculated using the formula: Area = (1/2) * base * height = (1/2) * 6 * 8.