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In triangle ABC,  B = 30^\circ, AB = 150, and AC = 50 sqrt3. Find the sum of all possible values of BC.

 Apr 4, 2020
 #1
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Angle B

It is given as 30 degrees

Angle C

By law of sines:

\(\frac{sin(30^\circ)}{50\sqrt{3}}=\frac{sin(C^\circ)}{150}\)

asin(150*(sin(30)/(50*sqrt(3))) = 60

 

Solving, we get angle C = 60 degrees.

Angle A

Since all angles in a triangle add to 180, angle A is 180 - 30 - 60 = 90.

 

BC

To solve for BC, try all of these methods (you may have different results depending on the method)

 

 - Pythagorean theorem

 - 30 - 60 - 90 triangle

 - Law of sines

 - Law of cosines

 

The answer is all the different values of BC added up.

 Apr 4, 2020
 #2
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Thanks! Still confused though. Isn't there only one answer as you found the angles already?

 Apr 5, 2020
 #3
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0

I think there is only one.


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