Trigonometry Examples

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

Substitute the name of each side into the definition of the cosine function.

Set up the equation to solve for the hypotenuse, in this case ${\displaystyle c}$.

Substitute the values of each variable into the formula for cosine.

The value of ${\displaystyle \cos \left(60\right)}$ is ${\displaystyle \frac{1}{2}}$.

Multiply the numerator by the reciprocal of the denominator.

Multiply ${\displaystyle 3}$ by ${\displaystyle 2}$.

Use the Pythagorean theorem to find the unknown side. In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (the two sides other than the hypotenuse).

Solve the equation for ${\displaystyle b}$.

Substitute the actual values into the equation.

Raise ${\displaystyle 6}$ to the power of ${\displaystyle 2}$.

Raise ${\displaystyle 3}$ to the power of ${\displaystyle 2}$.

Multiply ${\displaystyle -1}$ by ${\displaystyle 9}$.

Subtract ${\displaystyle 9}$ from ${\displaystyle 36}$.

Rewrite ${\displaystyle 27}$ as ${\displaystyle 3^2\cdot 3}$.

Pull terms out from under the radical.