Answer to Question #146192 in Trigonometry for Raffy

Question #146192
Is it possible to find a spherical triangle having the following sides? Explain why?

a = 120° b = 125° c = 130°
1
Expert's answer
2020-11-25T17:59:16-0500

yes , it is possible

by the law of cosines of sides and

law of sines



now ,

using law of cosines for sides :

cos a = cos b cos c + sin b sin c cosA

cos 120°\degree = cos 125°\degreecos 130°\degree + sin 125°\degree sin 130°\degree cosA

A = 77°\degree93'

using law of sines:

sinCsinc\frac{sinC}{sinc} = sinAsina\frac{sinA}{sina}


sinCsin130°\frac{sinC}{sin130\degree} = sin77°93sin120°\frac{sin77\degree93'}{sin120\degree}


C = 60°\degree48'


sinBsinb\frac{sinB}{sinb} = sinAsina\frac{sinA}{sina}


sinBsin125°\frac{sinB}{sin125\degree} = sin77°93sin120°\frac{sin77\degree93'}{sin120\degree}


B = 68°\degree51'


now we also can see spherical excess

E = (A+B+C) - 180°\degree

E = (77°\degree93' + 68°\degree51' + 60°\degree48' )-180°\degree

E = 26°\degree92'


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