Special Right Triangles

Front

What is a 45°-45°-90° triangle?

Back

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

Front

What is a 30°-60°-90° triangle?

Back

A special right triangle with angles of 30°, 60°, and 90°. The ratio of the lengths of the sides opposite these angles is 1:√3:2.

Front

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

Back

In a 45°-45°-90° triangle, if each leg has a length of 'a', then the hypotenuse has a length of 'a√2'.

Front

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

Back

In a 30°-60°-90° triangle, if the shortest side (opposite the 30° angle) is 'x', then the side opposite the 60° angle is 'x√3', and the hypotenuse is '2x'.

Front

If one leg of a 45°-45°-90° triangle is 24 in., what is the length of the hypotenuse?

Back

The hypotenuse is 24√2 in.

Front

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

Back

The shorter leg is 5 in.

Front

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

Back

Area = (1/2) * base * height.

Front

If the legs of a 45°-45°-90° triangle are each 10 in., what is the length of the hypotenuse?

Back

The hypotenuse is 10√2 in.

Front

In a 30°-60°-90° triangle, if the longer leg is 12 in., what is the length of the shorter leg?

Back

The shorter leg is 12/√3 or 4√3 in.

Front

What is the Pythagorean theorem?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c².