Question 290049: Solve for all possible triangles that satisfy a=9, b=13, measure of angle b=67 degrees. Round all values to the nearest tenth.
I know it is a lot of work, so i did part of it already :]
Since you know 2 sides and an angle. I can use law of sine to find a second angle. Since all the interior angles of a triangle is equal to 180 degrees, I can find the third angle. After this, I'm not too sure how to find the possible "multiple" types of triangles there are. Please help! Thank-you!
Answer by dabanfield(803)   (Show Source):
You can put this solution on YOUR website! Solve for all possible triangles that satisfy a=9, b=13, measure of angle b=67 degrees. Round all values to the nearest tenth.
I know it is a lot of work, so i did part of it already :]
Since you know 2 sides and an angle. I can use law of sine to find a second angle. Since all the interior angles of a triangle is equal to 180 degrees, I can find the third angle. After this, I'm not too sure how to find the possible "multiple" types of triangles there are. Please help! Thank-you!
You're doing GREAT!. You can find angle "a" using the law of sines:
(sin a)/9 = (sin 67)/13
Once you have angle "a" (the angle with sin(a) above) then you can find angle "c" as you said by subtracting 67 and angle "a" from 180.
Now that you have angle "c" you can find side "c" by:
(sin 67)/13 = (sin c)/c
Now you have all three sides and all three angles. Based on the side-side-side congruence theorem this defines a unique triangle.
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