Question 212761
In triangle ABC, A=27 degrees 35' , B=78 degrees 23' , and c= 19.  Find  a and round to the nearest tenth.


a)8.6
b)9.2
c)12.8
d)19.4


Step 1.  Convert angles A and B to decimal form (where 1 degree = 60 minutes)


{{{A=27+35/60=27.583}}} degrees


{{{B=78+23/60=78.333}}} degrees


Step 2.  Use a property of a triangle where sum of the angles of a triangle is 180 degrees to find angle C

{{{C=180-A-B=180-27.583 -78.333=74.084 }}}


{{{C=74.084}}}


Step 2.  To find c, Law of Sines


{{{sin(A)/a=sin(B)/b=sin(C)/c}}}


{{{sin(A)/a=sin(C)/c}}}


{{{a=c*sin(A)/sin(C)}}}


{{{a=19*sin(27.583)/sin(74.084)}}}


{{{a=9.148=9.2}}}


Step 3.  ANSWER IS 9.2 or (b)

I hope the above steps were helpful. 

 
And good luck in your studies!


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Respectfully,
Dr J