Law of Cosines

For the triangle figure, what is the length of the third side?

Hint
Law of Cosines:
$$$b^2=a^2+c^2-2ac\:cos\:B$$$
Hint 2
For oblique (non-right) triangles, use the Law of Cosines to determine unknown sides:
$$$a^2=b^2+c^2-2bc\:cos\:A$$$
$$$b^2=a^2+c^2-2ac\:cos\:B$$$
$$$c^2=a^2+b^2-2ab\:cos\:C$$$
Thus, to find side $$b$$ :
$$$b^2=a^2+c^2-2ac\:cos\:B$$$
$$$b^2=15^2+25^2-2(15)(25)\:cos\:77^{\circ}$$$
$$$b^2=225+625-(750)(0.2249)$$$
$$$b=\sqrt{850-168.71}=\sqrt{681.29}=26.1$$$
26.1