SOLUTION: Solve the triangle for A = 36°, B = 98°, c = 16.

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Question 1076218: Solve the triangle for
A = 36°, B = 98°, c = 16.
Found 2 solutions by Alan3354, Edwin McCravy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the triangle for
A = 36°, B = 98°, c = 16.
=============
Step 1, find the 3rd angle.
Then use the Law of Sines.
===========
It's arithmetic.

Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!


We find the third angle C by the fact that the three angles
of any triangle must have sum 180°.

 A  +  B  + C = 180°
36° + 98° + C = 180°  
     134° + C = 180°
            C = 46°

So we fill in angle C as 46°

 

Next we use the law of sines:



We substitute what we know so far:

eq. 1:  

Using the 1st and 3rd expressions of eq. 1:

matrix%281%2C3%2Ca%2Fsin%28%2236%B0%22%29%2C%22%22=%22%22%2C16%2Fsin%28%2246%B0%22%29%29

Cross-multiply:

matrix%281%2C3%2Ca%2Asin%28%2246%B0%22%29%2C%22%22=%22%22%2C16%2Asin%28%2236%B0%22%29%29



Guess we'll just round that off to a = 13.1, and fill that in:

 


Using the 2nd and 3rd expressions of eq. 1:

matrix%281%2C3%2Cb%2Fsin%28%2298%B0%22%29%2C%22%22=%22%22%2C16%2Fsin%28%2246%B0%22%29%29

Cross-multiply:

matrix%281%2C3%2Cb%2Asin%28%2246%B0%22%29%2C%22%22=%22%22%2C16%2Asin%28%2298%B0%22%29%29



Guess we'll just round that off to b = 22.0  and fill that in:



And now we're done.

Edwin