CB 4-17b Special Right Triangles Review

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

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

Back

The hypotenuse is x√2.

Front

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

Back

The longer leg is x√3.

Front

If the hypotenuse of a 30°-60°-90° triangle is 20, what is the length of the shorter leg?

Back

The shorter leg is 10.

Front

What is the relationship between the angles in a right triangle?

Back

The sum of the angles in a triangle is always 180°. In a right triangle, one angle is 90°, so the other two angles must sum to 90°.

Front

In a 45°-45°-90° triangle, if the hypotenuse is 10√2, what is the length of each leg?

Back

Each leg is 10.

Front

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

Back

Area = 1/2 * base * height.

Front

If the legs of a 30°-60°-90° triangle are 5 and 5√3, what is the length of the hypotenuse?

Back

The hypotenuse is 10.

Front

What is the Pythagorean theorem?

Back

In a right triangle, a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides.