What laws do i use, cosine, sine? On a triangle, if a=7, and b=4 and gamma=110 degrees find the remaining side

Question

and angles

Answer 1

Triangle ABC
AC = 4
BC = 7
Enclosed angle, C = 110°
Remaining side , AB = x
x² = 7² + 4² - 56 cos 110°
x = 9.17
AB = 9.17
9.17 / sin110° = 4 / sin B
sin B = 4 sin 110° / 9.17
B = 24.2°
A = 180° - (24.2 + 110)°
A = 45.8°

Answer 2

You actually use both.

To find the remaining side, use cosine law

c^2 = a^2 + b^2 - 2abcosgamma
c^2 = 49 + 16 - 2(7)(4)cos110
c = 9.1735

Use sine law to find the other angles:

sin 110 / 9.1735 = sin A / 7
A = 45.81

sin 110/9.1735 = sin B / 4
B = 24.19