Special Right Triangles and Trig Functions

Front

What is a special right triangle?

Back

A special right triangle is a right triangle with specific angle measures that allow for easy calculation of side lengths. 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 sides are in the ratio 1:1:√2. If each leg is of length 'x', the hypotenuse will be 'x√2'.

Front

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

Back

In a 30-60-90 triangle, the sides are in the ratio 1:√3:2. The side opposite the 30° angle is 'x', the side opposite the 60° angle is 'x√3', and the hypotenuse is '2x'.

Front

How do you find the length of the hypotenuse in a 45-45-90 triangle?

Back

To find the hypotenuse, multiply the length of one leg by √2.

Front

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

Back

To find the longer leg, multiply the length of the shorter leg (opposite the 30° angle) by √3.

Front

What is the sine function in relation to a right triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine function in relation to a right triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the tangent function in relation to a right triangle?

Back

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Front

If the legs of a 45-45-90 triangle are each 7, what is the length of the hypotenuse?

Back

The hypotenuse is 7√2.

Front

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

Back

The longer leg is 5√3.