Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths. The two main types are the 45°-45°-90° triangle and the 30°-60°-90° triangle.

Tags

CCSS.8.G.B.8

Front

What are the angle measures of a 45°-45°-90° triangle?

Back

The angle measures are 45°, 45°, and 90°.

Tags

CCSS.8.G.B.8

Front

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

Back

The ratio of the sides is 1:1:√2, where the legs are equal and the hypotenuse is √2 times the length of each leg.

Tags

CCSS.8.G.B.8

Front

What are the angle measures of a 30°-60°-90° triangle?

Back

The angle measures are 30°, 60°, and 90°.

Tags

CCSS.HSG.CO.C.10

Front

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

Back

The ratio of the sides is 1:√3:2, where the side opposite the 30° angle is 1, the side opposite the 60° angle is √3, and the hypotenuse is 2.

Tags

CCSS.HSG.CO.C.10

Front

If one leg of a 45°-45°-90° triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Tags

CCSS.8.G.B.8

Front

If the hypotenuse of a 30°-60°-90° triangle is 10, what is the length of the side opposite the 30° angle?

Back

The length of the side opposite the 30° angle is 5.

Tags

CCSS.8.G.B.8

Front

If the side opposite the 60° angle in a 30°-60°-90° triangle is 6√3, what is the length of the hypotenuse?

Back

The length of the hypotenuse is 12.

Tags

CCSS.8.G.B.8

Front

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

Back

The sum of the angles in a right triangle is always 180°, with one angle being 90°.

Tags

CCSS.8.G.A.5

Front

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

Back

Divide the length of the hypotenuse by 2 to find the length of the leg opposite the 30° angle, and multiply by √3 to find the length of the leg opposite the 60° angle.

Tags

CCSS.HSG.CO.C.10