Special Right Triangles and Trig Ratios

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The sides opposite the 45° angles are equal, and the hypotenuse is √2 times the length of each leg.

Front

What is a 30-60-90 triangle?

Back

A special right triangle where the angles are 30°, 60°, and 90°. The side opposite the 30° angle is half the hypotenuse, and the side opposite the 60° angle is √3 times the length of the shorter leg.

Front

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

Back

If the legs are of length 'x', then the hypotenuse is x√2.

Front

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

Back

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

Front

How do you find the sine of an angle in a right triangle?

Back

Sine of an angle = Opposite side / Hypotenuse.

Front

How do you find the cosine of an angle in a right triangle?

Back

Cosine of an angle = Adjacent side / Hypotenuse.

Front

How do you find the tangent of an angle in a right triangle?

Back

Tangent of an angle = Opposite side / Adjacent side.

Front

What is the value of sin(30°)?

Back

sin(30°) = 1/2.

Front

What is the value of cos(30°)?

Back

cos(30°) = √3/2.

Front

What is the value of tan(30°)?

Back

tan(30°) = 1/√3.