Help with finding a missing angle

Question

Find the missing angle below. Estimate your answers to one decimal place.

  

             C

             ^

             |  \

        9.6 |     \

             |_____\

           D   14.4   E

 

 

(sorry about the terrible text triangle, it was the best I could do)

 

Answer 1

triangle CDE is a right triangle

find angle E

use the tangent function

tan=opposite/adjacent

tanE=9.6/14.4

tanE=0.666...

use the arctan function on your calculator or a table or the internet...

tan^-1E=0.666...

E=33.69006753º

E=33.7º

find angle C

90-33.69006753=56.30993

E=56.3º

or if you like you could use the tangent function for angle C with tan=14.4/9.6=1.5 and then use arctan function