Special Right Triangles

Front

What is a 30°-60°-90° triangle?

Back

A special right triangle where the angles measure 30°, 60°, and 90°. The sides are in the ratio 1:√3:2.

Front

What is a 45°-45°-90° triangle?

Back

A special right triangle where the angles measure 45°, 45°, and 90°. The sides are in the ratio 1:1:√2.

Front

What is the length of the hypotenuse in a 30°-60°-90° triangle if the shorter leg is 5?

Back

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

Front

What is the length of the longer leg in a 30°-60°-90° triangle if the shorter leg is 5?

Back

5√3 (The longer leg is √3 times the length of the shorter leg.)

Front

If the hypotenuse of a 45°-45°-90° triangle is 5√2, what is the length of each leg?

Back

5 (Each leg is equal to the hypotenuse divided by √2.)

Front

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

Back

Hypotenuse = leg × √2.

Front

In a 30°-60°-90° triangle, if the longer leg is 10, what is the length of the shorter leg?

Back

5 (The shorter leg is half the length of the hypotenuse.)

Front

What is the relationship between the angles and sides in a special right triangle?

Back

The angles determine the ratios of the sides, which are consistent for 30°-60°-90° and 45°-45°-90° triangles.

Front

How do you identify a 30°-60°-90° triangle?

Back

Look for one angle measuring 30° and another measuring 60°.

Front

How do you identify a 45°-45°-90° triangle?

Back

Look for two equal angles of 45°.