SOLUTION: The following facts are true about triangle ABC: [measure_angle_B=120 degrees, AC=x(sqroot3), BC=x How many choices are there for the measure of angle A?

Question 205114: The following facts are true about triangle ABC:
[measure_angle_B=120 degrees, AC=x(sqroot3), BC=x
How many choices are there for the measure of angle A?

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
The following facts are true about triangle ABC:
[measure_angle_B=120 degrees,
AC=x(sqroot3) (this is side "b",
BC=x (this is side a)
How many choices are there for the measure of angle A?
----
Using the Law of Sines you get:
sin(A)/a = sin(B)/b
-------------------
sin(A)/x = sin(120)/x(sqrt(3))
---
sin(A) = [sqrt(3)/2]/(sqrt(3))
sin(A) = (1/2)
---
So the measure of angle A could be 30 deg or it could be 150 deg
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Cheers,
Stan H.
Answer by Edwin McCravy(20086) (Show Source): You can put this solution on YOUR website!
Edwin's solution. Stanbon is wrong to say angle A could be 150�. It can only be 30�. Here's why:

By the law of sines: Cross-multiply: Divide both sides by We know that , so substituting: Write as a division: Invert and multiply There are two angles between 0� and 180� which have sine , they are 30� and 150�, but angle A cannot be 150�, because angle B is 120�, and that would make two angles in the same triangle with sum more than 180� which is impossible. So angle A can only be 30�. Edwin

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