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

If the shorter leg (opposite the 30° angle) is 'x', then the longer leg (opposite the 60° angle) is 'x√3', and the hypotenuse is '2x'.

Front

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

Back

Divide the length of the longer leg by √3 and then multiply by 2.

Front

If the shorter leg of a 30-60-90 triangle is 7, what is the length of the longer leg?

Back

The longer leg is 7√3.

Front

If the hypotenuse of a 30-60-90 triangle is 14, what is the length of the shorter leg?

Back

The shorter leg is 7.

Front

What is the formula to find 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 = Shorter leg × 2.

Front

How do you find the missing angle in a triangle?

Back

The sum of angles in a triangle is 180°. Subtract the known angles from 180° to find the missing angle.

Front

If one angle in a triangle is 90° and another is 36.9°, what is the third angle?

Back

The third angle is 53.1°.

Front

What is the value of sin(30°)?

Back

sin(30°) = 1/2.