Solve for the remaining sides and angles if possible As in t

Solve for the remaining side(s) and angle(s) if possible. As in the text, (?, a), (?, b) and (?, c) are angle-side opposite pairs:

Solution

using sine law

sinAlpha/a=sinBeta/b

sin50/25= sin beta/12.5

sin beta=12.5 sin50/25= 22.5 degree

gamma=180-alpha-beta= 107.5 degree

sinalpha/a=sin gamma/c

sin 50/25= sin 107.5/c

c= 25 sin 107.5/sin 50= 31.1