SOLUTION: The perimeter of a triangle ABC is 500m. A=40 degrees and B= 60 degrees. Find the distance AB. Thank You! :)

Question 483871: The perimeter of a triangle ABC is 500m. A=40 degrees and B= 60 degrees. Find the distance AB. Thank You! :)
Answer by cleomenius(959) (Show Source): You can put this solution on YOUR website!
To solve this, we need to use the law of sins; it states "The sides of a triangle are to one another in the same ratio as the sines of their opposite angles".
So, fist I found the sines of the three angles:
A =40 degrees = sine is .642
B = 60 degrees = sine is .86
C = 80 degrees = sine is .985
Next, I added up the three to obtain 2.487.
So that is the total, to find the proportion of 500 for each side, I multiplied that angles sine/ 2.487 by 500. This resulted in:
a = 129.1
b = 172.9
c = 198.0
The three sides do total 500.
Cleomenius.

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