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 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 legs of a 45°-45°-90° triangle are each 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

How do you find the length of the hypotenuse in a 30°-60°-90° triangle if the shorter leg is 5?

Back

The hypotenuse is 10 (twice the length of the shorter leg).

Front

What is the formula to find the length of the legs in a 45°-45°-90° triangle if the hypotenuse is known?

Back

Each leg = hypotenuse / √2.

Front

What is the measure of the angles in a 30°-60°-90° triangle?

Back

30°, 60°, and 90°.

Front

If the hypotenuse of a 45°-45°-90° triangle is 8, what is the length of each leg?

Back

Each leg is 8/√2 or 4√2.

Front

What is the length of the longer leg in a 30°-60°-90° triangle if the shorter leg is 6?

Back

The longer leg is 6√3.

Front

What type of triangle is formed by the angles 45°, 45°, and 90°?

Back

It is a 45°-45°-90° triangle.

Front

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

Back

The shorter leg is 6.