special right triangles

Front

What are the two types of special right triangles?

Back

The two types of special right triangles are 30°-60°-90° triangles and 45°-45°-90° triangles.

Front

What is the ratio of the sides in a 30°-60°-90° triangle?

Back

In a 30°-60°-90° triangle, the ratio of the lengths of the sides opposite the 30°, 60°, and 90° angles is 1:√3:2.

Front

What is the ratio of the sides in a 45°-45°-90° triangle?

Back

In a 45°-45°-90° triangle, the ratio of the lengths of the legs is 1:1, and the hypotenuse is √2 times the length of each leg.

Front

How do you find the length of the hypotenuse in a 45°-45°-90° triangle if one leg is 8?

Back

The hypotenuse is 8√2.

Front

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

Back

The length of the shorter leg (opposite the 30° angle) is 5.

Front

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

Back

The length of the longer leg (opposite the 60° angle) is 4√3.

Front

In a 30°-60°-90° triangle, if the longer leg is 6√3, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 12.

Front

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

Back

The hypotenuse = leg length × √2.

Front

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

Back

The hypotenuse is x√2.

Front

How do you determine the length of x in a 30°-60°-90° triangle if the hypotenuse is known?

Back

x (the shorter leg) = hypotenuse/2 and the longer leg = shorter leg × √3.