Explore 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 legs are of equal length, and the hypotenuse is √2 times the length of a leg.

Front

How do you find the length of the second leg in a 45-45-90 triangle if one leg is known?

Back

Use the same length for the second leg.

Front

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

Back

Divide the length of the hypotenuse by √2.

Front

What is the relationship between the legs and the hypotenuse in a 45-45-90 triangle?

Back

The hypotenuse is √2 times the length of each leg.

Front

What is a 30-60-90 triangle?

Back

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

Front

How do you find the length of the long leg in a 30-60-90 triangle if the hypotenuse is known?

Back

Multiply the length of the hypotenuse by √3/2.

Front

How do you find the length of the short leg in a 30-60-90 triangle if the hypotenuse is known?

Back

Divide the length of the hypotenuse by 2.

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the short leg?

Back

6 (12 divided by 2).

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the long leg?

Back

6√3 (12 multiplied by √3/2).

Front

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

Back

Hypotenuse = leg × √2.