Special Right Triangles

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures and side length ratios, making calculations easier. The two main types are the 45-45-90 triangle and the 30-60-90 triangle.

Front

What are the side ratios of a 45-45-90 triangle?

Back

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

Front

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

Back

Hypotenuse = leg × √2.

Front

What are the side ratios of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2, where 1 is the length of the side opposite the 30° angle.

Front

What is the formula to find the length of the longer leg in a 30-60-90 triangle?

Back

Longer leg = shorter leg × √3.

Front

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

Back

Hypotenuse = 2 × shorter leg.

Front

If one leg of a 45-45-90 triangle is 10, what is the length of the hypotenuse?

Back

Hypotenuse = 10 × √2 = 10√2.

Front

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

Back

Shorter leg = 12 / 2 = 6.

Front

If the longer leg of a 30-60-90 triangle is 9√3, what is the length of the hypotenuse?

Back

Hypotenuse = 2 × (9√3 / √3) = 18.

Front

What is the value of x if x is the hypotenuse of a 45-45-90 triangle with legs of length 5?

Back

x = 5√2.