What is the length of side c, given a = 10, b = 8, and c = 105°?

We can calculate using cosinus method in triangle

c² = a² + b² - 2ab cos c

Plug in the number to the formula

c² = a² + b² - 2ab cos c

c² = 10² + 8² - 2 (10) (8) cos 105°

c² = 100 + 64 - 160 cos 105°

c² = 164 - 160 (-0.26)

c² = 164 + 41.6

c² = 205.6

c = √205.6

c = 14.34

C is 14.34 unit length