Special Right Triangles

Front

What are the properties of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the legs are of equal length, and the length of the hypotenuse is √2 times the length of a leg.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

Multiply the length of a leg by √2.

Front

What is the relationship between the legs and hypotenuse in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the short leg, and the length of the long leg is √3 times the length of the short leg.

Front

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

Back

Multiply the length of the short leg by √3.

Front

What is the formula to 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 length of the legs in a 45-45-90 triangle if the hypotenuse is 8?

Back

Each leg is 8/√2, which simplifies to 4√2.

Front

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

Back

The hypotenuse is 2 times the short leg, so it is 8.

Front

What is the length of the long leg in a 30-60-90 triangle if the short leg is 5?

Back

The long leg is 5√3.

Front

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

Back

Divide the length of the hypotenuse by 2 to find the short leg, then multiply the short leg by √3 to find the long leg.

Front

What is the significance of the angles in a 45-45-90 triangle?

Back

The angles are both 45 degrees, indicating that the triangle is isosceles.