Answer to Question #146192 in Trigonometry for Raffy

Question

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

a = 120° b = 125° c = 130°

Answer 1

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$\degree$cos 130$\degree$ + sin 125$\degree$ sin 130$\degree$ cosA

A = 77$\degree$93'

using law of sines:

$\frac{sinC}{sinc}$ = $\frac{sinA}{sina}$

$\frac{sinC}{sin130\degree}$ = $\frac{sin77\degree93'}{sin120\degree}$

C = 60$\degree$48'

$\frac{sinB}{sinb}$ = $\frac{sinA}{sina}$

$\frac{sinB}{sin125\degree}$ = $\frac{sin77\degree93'}{sin120\degree}$

B = 68$\degree$51'

now we also can see spherical excess

E = (A+B+C) - 180$\degree$

E = (77$\degree$93' + 68$\degree$51' + 60$\degree$48' )-180$\degree$

E = 26$\degree$92'