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   Using Trigonometry to find and unknown angle


 

  • In this tutorial we will be using the Sin, Cos and Tan formulas

 


 

Example:  Find the value of marked angle (correct to the nearest degree)

    

   

                                                                  STEP 1  Look at the angle
    

                                                                  STEP 2 Label the given sides
     

                                                                              Hypotenuse = 10 cm
     

                                                                              Opposite = 6 cm
    

                                                                  STEP 3 Formula
     

                                                                              Sin x = O/H
    

                                                                  STEP 4  Substitute
     

                                                                              Sin x = 6/10
     

                                                                              Sin x = 0.6 (leave this answer in your calculator)
           

                                                                                   x = Sin^(-1) 0.6  (Sin^(-1) means the inverse of Sin.  This is done                          
                                                                                                              on the calculator by pressing , shift, 2nd f or          
                                                                                                              inv  sin)
    

                                                                  STEP 5 Answer
     

                                                                                   x = 36.87
     

                                                                                   x = 37 ̊

 

 


 

Example
    

  

                                                                 STEP 1  Look at the angle
    

                                                                 STEP 2 Label the given sides
     

                                                                             Adjacent = 22 m
        

                                                                             Opposite = 16 m
    

                                                                 STEP 3 Formula
     

                                                                             Tan x = O/A
    

                                                                 STEP 4  Substitute
     

                                                                             Tan x = 16/22
     

                                                                             Tan x = 0.7272….  (leave this answer in your calculator)
           

                                                                                   x = Tan^(-1) 0.7272..  ( With your answer on the calculator
 

                                                                                                                        press your , shift, 2nd f or   inv  sin to get your answer)
    

                                                                 STEP 5 Answer
     

                                                                                   x = 36.027
     

                                                                                   x = 36 ̊
 

 

                                             

                                                      Practice Exercises

 


 

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