GEO Special Right Triangles

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 : √3 : 2.

Front

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

Back

In a 30-60-90 triangle, if the shortest side (opposite the 30° angle) is 'x', then the longer leg (opposite the 60° angle) is 'x√3', and the hypotenuse is '2x'.

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are both 45 degrees and the right angle is 90 degrees. The sides are in the ratio 1 : 1 : √2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if each leg is 'x', then the hypotenuse is 'x√2'.

Front

If the hypotenuse of a 30-60-90 triangle is 10, what is the length of the shorter leg?

Back

5 (since the shorter leg is half the hypotenuse).

Front

If the longer leg of a 30-60-90 triangle is 6√3, what is the length of the hypotenuse?

Back

12 (the hypotenuse is double the shorter leg, which is 6).

Front

In a 30-60-90 triangle, if the shorter leg is 4, what is the length of the longer leg?

Back

4√3 (the longer leg is the shorter leg multiplied by √3).

Front

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

Back

Hypotenuse = leg × √2.

Front

If one leg of a 45-45-90 triangle is 7, what is the length of the hypotenuse?

Back

7√2.

Front

In a 30-60-90 triangle, if the longer leg is 10√3, what is the length of the hypotenuse?

Back

20 (the hypotenuse is double the shorter leg, which is 10).