Special Right Triangles

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees. The lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

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

Back

Multiply the length of the leg by √2.

Front

What is a 30-60-90 triangle?

Back

A 30-60-90 triangle is a right triangle with angles measuring 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1:√3:2.

Front

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

Back

Multiply the length of the short leg by 2.

Front

How do you find the long leg of a 30-60-90 triangle if you know the length of the short leg?

Back

Multiply the length of the short leg by √3.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1 (short leg) : √3 (long leg) : 2 (hypotenuse).

Front

If the short leg of a 30-60-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4 multiplied by 2, which equals 8.

Front

If the short leg of a 30-60-90 triangle is 4, what is the length of the long leg?

Back

The long leg is 4 multiplied by √3, which is approximately 6.93.

Front

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

Back

Hypotenuse = leg length × √2.

Front

What is the formula to find the long leg in a 30-60-90 triangle?

Back

Long leg = short leg length × √3.