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 lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30°, 60°, and 90°. The length of the side opposite the 30° angle is half the hypotenuse, and the length of the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

If the leg of a 45-45-90 triangle is 5, what is the length of the hypotenuse?

Back

5√2

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the shorter leg?

Back

5 (half of the hypotenuse).

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

If the shorter leg is x, then the longer leg is x√3 and the hypotenuse is 2x.

Front

Find the length of the hypotenuse in a 45-45-90 triangle with legs of length 4.

Back

4√2

Front

In a 30-60-90 triangle, if the longer leg is 6√3, what is the length of the hypotenuse?

Back

12 (the longer leg is √3 times the shorter leg).

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

Hypotenuse = leg × √2.

Front

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

Back

3√3.

Front

What is the value of y in a 45-45-90 triangle if the hypotenuse is 8√2?

Back

8 (the legs are equal to the hypotenuse divided by √2).