Special Right Triangles (30-60-90 & 45-45-90)

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30 degrees, 60 degrees, and 90 degrees. The sides are in the ratio 1 : @@rac{{ ext{√3}}}{{2}} : 2.

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are both 45 degrees and 90 degrees. The sides are in the ratio 1 : 1 : @@ ext{√2}.

Front

What is the formula for the length of the hypotenuse in a 30-60-90 triangle?

Back

The hypotenuse is twice the length of the shorter leg (1). If the shorter leg is 'a', then hypotenuse = 2a.

Front

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

Back

Front

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

Back

Both legs are equal in length. If one leg is 'a', then the other leg is also 'a'.

Front

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

Back

Front

What is the longest side of a right triangle called?

Back

The longest side is called the hypotenuse.

Front

If the shorter leg of a 30-60-90 triangle is 5, what is the length of the longer leg?

Back

Front

If the legs of a 45-45-90 triangle are each 6, what is the length of the hypotenuse?

Back

Front

What is the value of 'a' in a 30-60-90 triangle if the hypotenuse is 12?

Back

The shorter leg 'a' is 6.