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 a 30°-60°-90° triangle?

Back

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

Front

Find the length of the hypotenuse in a 45°-45°-90° triangle with legs of length 10.

Back

10√2

Front

Find the length of the longer leg in a 30°-60°-90° triangle if the shorter leg is 4.

Back

4√3

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

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

Back

5√2

Front

What is the Pythagorean theorem?

Back

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

Front

Find the missing side in a right triangle with sides 3 and 4.

Back

5 (using the Pythagorean theorem).

Front

What is the sum of the angles in any triangle?

Back

180°.

Front

If a triangle has angles of 30° and 60°, what is the third angle?

Back

90°.