Calculus/hi

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Expert: - 3/10/2009


Question
how do you solve the triangle?? (rounded two decimal places)

b=17.8
c=28.3
B= 27 degrees


there are two possibilities and
one side i get 46.05 for C and for A i get 106.95
using law of sines i got little a at about 37.32

and the other possibility i got 133.95 degrees for C and for A i got 19.05 degrees. and using law of sines I got little a as 12.83..

what am i doing wrong.. i've worked on this problem for so long and i can't figure out what i'm doing wrong.. thanks

Answer

Triangles
Since we know angle B, the law of cosines says that
a² + c² -2ac*cos(B) = b².

This will reduce to a quadratic equation in a of the form
da² + ea + f = 0 where d, e, and f are the constants
d = 1, e = -2c*cos(B), and f = c² - b².

The angle B in radians is 0.471238898.
Doing this, the cos(B) = 0.891006524.
{ I just cut those two values out of Excel and pasted them in.
That's why there's so many places. }

The answers are 37.5451507 and 12.88581857 { if no rounding is done; I let Excel use the celss I gave with the previous values }.

It looks like you are right in both cases.  Given an angle and two sides, one across from the angle, two triangles could be made.  
Just a moment and I'll make a picture for you.

I'm sure if C1 and C2 were found, the sum of the two of them
would be 180°, or π radians.  

Scotto

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