SOLUTION: Use the Law of Sines to solve the​ triangle, if possible.
C=72degrees​, b=51​, c=50
find A, a, B
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-> SOLUTION: Use the Law of Sines to solve the​ triangle, if possible.
C=72degrees​, b=51​, c=50
find A, a, B
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Question 1131379: Use the Law of Sines to solve the triangle, if possible.
C=72degrees, b=51, c=50
find A, a, B Found 2 solutions by Boreal, Edwin McCravy:Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! C/sin C=50/sin 72=52.57
Therefore if b=51 51/sinB=52.57
so sin B=51/52.57, or 0.9701 and B=75.96 deg
That would make A 180-128.53=51.47 deg
and a would be a/sin 51.47=52.57
a=41.12
This is the ambiguous case SSA where there are 2 solutions.
The other tutor only gave one of the solutions. Here
are both solutions:
Substitute what's given:
Take the last two expressions as a equation
Cross-multiply
Divide both sides by 50
The sine is positive in QI and QII, so
B = 75.94844394° and B = 180°-75.94844394 = 104.0515561
Let's subscript the two possibilities for angle B like this:
B1 = 75.94844394° and B2 = 104.0515561°
Now we calculate the two possibilities for angle A:
Angle A1 = 180° - Angle B1 - Angle C
Angle A1 = 180° - 75.94844394° - 72°
Angle A1 = 32.05155605°
Angle A2 = 180° - Angle B2 - Angle C
Angle A2 = 180° - 104.0515561° - 72°
Angle A2 = 3.9484439°
Finally we calculate the two possibilities for side "a":
----------
and
Substitute what is now known:
and
which shortens to:
and and
Divide through by sin(72°)
and and
Edwin
