Question

How do you solve the triangle given A=25, B=78, a=13.7?

Answer 1

`(/_A,/_B,/_C) = (25^@,78^@,77^@)`
`(a,b,c)=(13.7,31.71,31.59)`
`color(white)("XXX")`(`b` and `c` are approximate)

Explanation:

If `/_A=25^@`
and `/_B=78^@`
then
`color(white)("XXX")/_C=180^@-(25^@+78^@)=77^@`

Given `a=13.7` and using the Law of Sines
`color(white)("XXX")b=a/(sin(/_A))*sin(/_B) ~~31.7085733`
and
`color(white)("XXX")c=a/(sin(/_A)) * sin(/_C) ~~31.58611706`