Trigonometry Examples

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 ${\displaystyle c}$.

Substitute the actual values into the equation.

Raise ${\displaystyle 12}$ to the power of ${\displaystyle 2}$.

Raise ${\displaystyle 5}$ to the power of ${\displaystyle 2}$.

Add ${\displaystyle 144}$ and ${\displaystyle 25}$.

Rewrite ${\displaystyle 169}$ as ${\displaystyle {13}^2}$.

Pull terms out from under the radical, assuming positive real numbers.

The angle ${\displaystyle B}$ can be found using the inverse sine function.

Substitute in the values of the opposite side to angle ${\displaystyle B}$ and hypotenuse ${\displaystyle 13}$ of the triangle.

Evaluate ${\displaystyle \arcsin \left(\frac{12}{13}\right)}$.

The sum of all the angles in a triangle is ${\displaystyle 180}$ degrees.

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