Calculating the Length of a Side in a Right Triangle…

There are two ways to calculate the length of a side in a right triangle:

•  The Pythagorean Theorem… Which is only applicable when 2 sides of the triangle are know and then it follows the formula, and when used, looks like this
• Using Trigonometric Ratios to Calculate the Length…. Which is only applicable when the length of one side and the degree of one acute angle are known. This process follows a series of steps starting with labelling the hypotenuse, the adjacent and the opposite of a triangle based off of the known acute angle. Then you must identify what side is known and what side needs to be known. Next, you must choose the corresponding primary trig ratio: Sine, Cosine, or Tangent. (It makes it easier to use SOH CAH TOA to determine what trig function to use.) Once you have chosen the corresponding trig function, you must write out the equation like so  . Then solve the equation by either cross multiplying or dividing to solve for the wanted length of a side. This process looks like so