Posted by **Jon** on Friday, March 7, 2008 at 1:30pm.

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

no solution.

- Trig -
**drwls**, Friday, March 7, 2008 at 2:21pm
According to the law of sines,

sin C = c* sin A/a = 0.2668

C = 15.5 degrees, or 164.5 degrees. Only the 15.5 is possible without exceeding 180 degrees for all angles. That means B = 180 - 35 - 15.5 = 129.5 degrees. There is only one solution in this case, although some side-side-angle specified triangles (like this one) have two solutions.

b = sin B* a/sin A = 57.8

- Trig( you confused me) -
**Jon**, Friday, March 7, 2008 at 2:54pm
I get the work part of it but for this question is it one solution or two?

- Trig( you confused me) -
**drwls**, Friday, March 7, 2008 at 7:40pm
What I tried to say is that sometimes when two adjacent sides of a triangle are specified, along with the angle adjacent to one side, two solutions are possible. This called the "ambiguous Side-Side-Angle" case. This is a Side-Side-Angle case, but it turns out that only one solution is possible anyway. One of the two computed angles from the law of sines is too large to make a triangle possible.

- Trig -
**drwls**, Friday, March 7, 2008 at 7:35pm
One

## Answer this Question

## Related Questions

- Math - check my answers :) - 1. Find the amplitude, if it exists, and the period...
- Math/Trig - Given A=56degrees, C=61degrees, and b=10.5, solve triangle ABC. If ...
- Math/Trig - Given A=56degrees, C=61degrees, and b=10.5, solve triangle ABC. If ...
- Math - For problems 1 and 2, determine how many solutions there are for each ...
- geometry - Triangle ABC is a right triangle such that m angle B= 90 degrees. If ...
- Trig - Consider a triangle ABC like the one below. Suppose that A=45 degress, B=...
- Algebra - Triangles ABC and DEF are similar. Find the area of triangle ABC. ...
- algebra - Triangles ABC and DEF are similar. Find the area of triangle ABC. ...
- Math - Determine whether the triangle has no/one/two solutions. Then Find and ...
- Math - Determine whether the triangle has no/one/two solutions. Then Find and ...