SOLUTION: in triangle ABC, A=27 degrees 35' , B=78 degrees 23' , and c=19.find a.round to the nearest tenth. a)8.6 b)9.2 c)12.8 d)19.4

Algebra ->  Trigonometry-basics -> SOLUTION: in triangle ABC, A=27 degrees 35' , B=78 degrees 23' , and c=19.find a.round to the nearest tenth. a)8.6 b)9.2 c)12.8 d)19.4      Log On


   

Question 212761: in triangle ABC, A=27 degrees 35' , B=78 degrees 23' , and c=19.find a.round to the nearest tenth.
a)8.6
b)9.2
c)12.8
d)19.4
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
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%2B35%2F60=27.583 degrees

B=78%2B23%2F60=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%28A%29%2Fa=sin%28B%29%2Fb=sin%28C%29%2Fc

sin%28A%29%2Fa=sin%28C%29%2Fc

a=c%2Asin%28A%29%2Fsin%28C%29

a=19%2Asin%2827.583%29%2Fsin%2874.084%29

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