SOLUTION: the measure of two angles are 100 degrees and 46 degrees. the length of the shortest sides of the triangle is 12. find the measure to the nearest integer and the lengths of the oth

Algebra ->  Triangles -> SOLUTION: the measure of two angles are 100 degrees and 46 degrees. the length of the shortest sides of the triangle is 12. find the measure to the nearest integer and the lengths of the oth      Log On


   

Question 733518: the measure of two angles are 100 degrees and 46 degrees. the length of the shortest sides of the triangle is 12. find the measure to the nearest integer and the lengths of the other two sides
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The measures of two angles of a triangle are 100%5Eo and 46%5Eo .
We know that the measures of all 3 angles add up to 180%5Eo, so the measure of the third angle is
180%5Eo-%28100%5Eo%2B46%5Eo%29=180%5Eo-146%5Eo=34%5Eo
In a triangle, the shortest side is opposite the smallest angle and the longest side is opposed the largest angle, so the shortest side is opposite the 34%5Eo angle.
The law of sines, says that in a triangle the ratio of the length of a side and the sine of the opposite angle is constant.
That means that the lengths, a, and b of the other two sides are related by
12%2Fsin%2834%5Eo%29=a%2Fsin%28100%5Eo%29=b%2Fsin%2846%5Eo%29
Using approximate values for the sines of those angles.
12%2F0.559=a%2F0.985=b%2F0.719
Solving the equations that can be split from there,
12%2F0.559=a%2F0.985 --> 12%2F0.559%2A0.985=a --> highlight%28a=21.1%29 (rounded)
12%2F0.559=b%2F0.719 --> 12%2F0.559%2A0.719=b --> highlight%28b=15.4%29 (rounded)