SOLUTION: In triangle ABC A=35 degrees, a=43 and c=20. Determine whether triangle ABC has no solution, one solution, or two solutions. Then solve the triangle. Round to the nearest tenth.

Algebra.Com
Question 149726: In triangle ABC A=35 degrees, a=43 and c=20. Determine whether triangle ABC has no solution, one solution, or two solutions. Then solve the triangle. Round to the nearest tenth.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
In triangle ABC A=35 degrees, a=43 and c=20. Determine whether triangle ABC has no solution, one solution, or two solutions. Then solve the triangle. Round to the nearest tenth.






In solving the ambiguous case, "Angle-Side-Side", "ASS", 
we use the law of sines in this fashion:



Solve for 

1. If this is greater than 1 there are no solutions.
2. If this is less than 1, we have either one or two solutions 
3. In the rare case this equals exactly 1, the
    is 90°, and you 
   solve it as a right triangle.

In case 2, 

I. use the inverse sine button on your calculator to find one 
certain possibility for the .

II. Find the supplement of the angle found in step I, by subtracting
    from 180°.

III. Add the result of step II to the given angle and subtract from
     180°.

IV.  If the result of III is negative there is only one solution. If it
     is positive then there are two solutions, one with the result of II
     and one with the result of III for the .


In your problem we use the law of sines in this fashion:



°



 is the unknown angle 





Solve for 



This is less than 1, so we have case 2 above, and
there is either one or two solutions. So

I. We use the inverse sine button on the calculator to find one 
certain solution for the angle C.

angle C = 15.47273197°

II. Find the supplement of that angle, by subtracting from 180°:

180° - 15.47273197° = 164.527268°

III. Add the result of step II to the given angle and subtract from
     180°.

164.527268° + 35° = 199.527268°

180° - 199.527268° = -19.52726803°.

 
IV.  This result is negative, so there is only one solution. 

Now to find the other parts.  We can find angle B by adding
the given angle A = 35° to Angle C = 15.47273197°, and then
subtracting from 180° to find Angle B:

35° + 15.47273197° = 50.47273197°

180° - 50.47273197° = 129.527268° = Angle B

Using the law of sines again to find side 





So we round everything to the nearest tenth:

angle C = 15.5°, angle B = 129.5°, side b = 57.8

Edwin
RELATED QUESTIONS

In /\ ABC, A=35 degrees, a=43, c=20. Determine whether /\ ABC has no solution, one... (answered by stellababy)
I have two questions. 1. Find the area of triangle ABC if A=56 degrees, b=20 ft, and... (answered by Alan3354,jojo14344)
Determine whether the triangle has no solution, one solution, or two solutions. A=29°,... (answered by Aldorozos)
Determine whether this triangle has no solution, one solution, or two solutions. A= 60°,... (answered by Aldorozos)
Triangle ABC has vertices A(0,4), B(1,2), and C(4,6). Determine whether triangle ABC is a (answered by khwang)
triangle ABC has vertices at A(7,-4) B(-1,2) C(5,-6). determine whether the triangle has... (answered by mukhopadhyay)
1. from the top of the cliff, a geologist spots a dry riverbed. the measurement of the... (answered by solver91311)
Two side and an angle are given. Determine whether the given information results in one... (answered by Edwin McCravy)
in the following exercise, two sides and an angle are given, first determine whether the... (answered by greenestamps)