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.

Tags

CCSS.HSG.CO.C.10

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.

Tags

CCSS.8.G.B.8

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.)

Tags

CCSS.8.G.B.8

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.)

Tags

CCSS.HSG.CO.C.10

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.)

Tags

CCSS.8.G.B.8

Front

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

Back

Hypotenuse = leg × √2.

Tags

CCSS.8.G.B.8

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.)

Tags

CCSS.8.G.B.8

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.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

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

Tags

CCSS.2.G.A.1

Front

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

Back

Look for two equal angles of 45°.

Tags

CCSS.8.G.B.8