Special Right Triangles

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles measure 30°, 60°, and 90°. The sides are in the ratio 1 : √3 : 2.

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles measure 45°, 45°, and 90°. The sides are in the ratio 1 : 1 : √2.

Front

In a 30-60-90 triangle, if the shortest side (opposite the 30° angle) is x, what is the length of the longer leg (opposite the 60° angle)?

Back

The longer leg is x√3.

Front

In a 30-60-90 triangle, if the hypotenuse is 2x, what is the length of the shorter leg?

Back

The shorter leg is x.

Front

In a 30-60-90 triangle, if the longer leg is y, what is the length of the hypotenuse?

Back

The hypotenuse is (2/√3) * y.

Front

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

Back

Both legs are equal in length, and the hypotenuse is √2 times the length of each leg.

Front

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

Back

Each leg is 10/√2 or 5√2.

Front

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

Back

Area = 1/2 * base * height.

Front

In a 30-60-90 triangle, if the shorter leg is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 8.

Front

If the longer leg of a 30-60-90 triangle is 6√3, what is the length of the shorter leg?

Back

The shorter leg is 6.