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 length of 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

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

Back

The hypotenuse is 4√2.

Front

In a 30-60-90 triangle, if the shorter leg is 5, what is the length of the longer leg?

Back

The longer leg is 5√3.

Front

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

Back

Hypotenuse = leg × √2.

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The shorter leg is 6.

Front

What is the value of x in a 45-45-90 triangle if one leg is 8?

Back

x = 8√2.

Front

In a 30-60-90 triangle, if the longer leg is 14, what is the length of the shorter leg?

Back

The shorter leg is 7.

Front

What is the area of a 45-45-90 triangle with legs of length 4?

Back

Area = (1/2) × leg × leg = (1/2) × 4 × 4 = 8.

Front

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

Back

The hypotenuse is 6.