Note that the same results are obtained when you use natural functions or logarithms of circular
4-11. Case II - Two Sides and an Opposite Angle. In solving a triangle where two sides and an
opposite angle are known, it is necessary to solve for one of the unknown angles using the sine law.
Next, you will solve for the third angle by subtracting the sum of the given angle and the solved-for
angle from 180. Then, by using the sine law, you can solve for the remaining unknown side.
Example: In Figure 4-19, side b of the triangle equals 135.2 feet, side a equals 196.6 feet, and angle A
equals 32 36' 40". Find angles B and C and side c.
Figure 4-19. Case II
Solution: Using the sine law, solve for angle B.
B = 21 45' 14" (by natural functions)
Then solve for angle C by subtracting the sum of angles A and B from 180€.
C = 180€-(32€ 36' 40"+21 45' 14") = 125€ 38' 06"