Special Right Triangles

Front

What is the relationship between the legs and hypotenuse in a 45-45-90 triangle?

Back

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

Front

How do you find the length of a leg in a 45-45-90 triangle if the hypotenuse is known?

Back

To find the length of a leg, divide the length of the hypotenuse by √2.

Front

What are the side lengths in a 30-60-90 triangle in relation to the short leg?

Back

In a 30-60-90 triangle, the short leg is x, the long leg is x√3, and the hypotenuse is 2x.

Front

How do you find the long leg in a 30-60-90 triangle if the short leg is known?

Back

To find the long leg, multiply the length of the short leg by √3.

Front

How do you find the hypotenuse in a 30-60-90 triangle if the short leg is known?

Back

To find the hypotenuse, multiply the length of the short leg by 2.

Front

What is the formula to calculate 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 Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b): c² = a² + b².

Front

In a 30-60-90 triangle, which side is the longest?

Back

The hypotenuse is the longest side in a 30-60-90 triangle.

Front

What is the value of the long leg in a 30-60-90 triangle if the short leg is 4?

Back

If the short leg is 4, the long leg is 4√3.

Front

If the hypotenuse of a 45-45-90 triangle is 10, what is the length of each leg?

Back

If the hypotenuse is 10, each leg is 10/√2 or 5√2.