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

Back

In a 30°-60°-90° triangle, the side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the shorter leg.

Front

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

Back

The hypotenuse is 4√2.

Front

If one leg of a 30°-60°-90° triangle is 5, what is the length of the hypotenuse?

Back

The hypotenuse is 10.

Front

What is the formula for finding the length of the hypotenuse in a 45°-45°-90° triangle?

Back

Hypotenuse = leg × √2.

Front

What type of triangle is formed by angles of 30°, 60°, and 90°?

Back

30°-60°-90° triangle.

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 length of the longer leg in a 30°-60°-90° triangle if the shorter leg is 3?

Back

The longer leg is 3√3.

Front

In a 45°-45°-90° triangle, if one leg is x, what is the length of the other leg?

Back

The other leg is also x.

Front

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

Back

Area = (1/2) × 4 × 4 = 8.