Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The sides opposite the 45° angles are equal, and the hypotenuse is √2 times the length of each leg.

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, the side opposite the 60° angle is √3 times the shortest side, and the hypotenuse is twice the shortest side.

Front

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

Back

Multiply the length of one leg by √2.

Front

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

Back

Divide the length of the hypotenuse by √2.

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.

Front

If one leg of a 45-45-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the side opposite the 30° angle?

Back

The side opposite the 30° angle is 5.

Front

What is the length of the side opposite the 60° angle in a 30-60-90 triangle if the shortest side is 8?

Back

The side opposite the 60° angle is 8√3.

Front

In a 45-45-90 triangle, if the hypotenuse is 8√2, what is the length of each leg?

Back

Each leg is 8.

Front

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

Back

The hypotenuse is 12/√3 * 2 = 8√3.