SOH CAH TOA is a mneumonic device used to help students remember the following formulas
sinX=opposite/hypotenuse cosX= adjacent/ hypotenuse tanX= opposite/ adjacent
where the hypotenuse is ALWAYS across from the right angle. The adjacent side "lies next to" the stated angle and the opposite side is located "across" from the stated angle.  For Example A, find the measure of side b ( also known as side AC) and side c ( also known as side AB) 1) Side b is the side opposite the given angle. Side a ( labeled 10 ft) is adjacent the given angle. Therefore you would use the tangent function as follows:
Tan(37) = b / 10. b is the unknown value we are searching for. You may label this with x or another variable if you choose.
Once you have set up on the formula, you can cross multiply to solve for the variable. b= [Tan (37) ] * 10 . This is the result of cross-multiplying. On the calculator, press the tan button followed by the given angle measurement. Then multiple by 10. b= 7.54 ( after rounding) 2) Find the measure of side c. Similar to problem 1. Use the given information to identify which formula to use and set up the equation. In this case, we are looking for the hypotenuse and are given the adjacent measurement so we would use cosine as follows: Cos 37 = 10 / c . (we are looking for c ) Solve for c by cross-multipying and setting the equation equal to c. c= 10/ cos 37 . It might be easier to evaluate the cos first on your graphing calculator. Then press 10 / {sec} {enter} ( Second + Enter places the previous answer on the screen) On the calculator to the left, enter Press 10 / ( cos 37) . Make sure you put cos of 37 in parenthesis or the calculator will follow the natural order of operations. c = 12.5 (when rounded) Example B 1) Find the measure of angle A. When you are looking for a leg, you use the trig functions. When you are looking for an angle, you would use the inverse trig functions. These problems are set up the same way. The difference(for our purposes) is the use of the calculator button. In relation to angle a, the opposite side is 6 and the adjacent side is 4 so we would use the tangent function as follows: tanA= 6/4 . Evaluate 6/4 first. Then hit second ( or shift) tan and type in the previous answer. On the calculator to the left you may enter {shift} {tan} {Ans} after evaluating 6/4. |
