Two sides and an angle are given below Determine whether the

Two sides and an angle are given below. Determine whether the given information results in one triangle, two triangles, or no triangle at all. Solve any triangle(s) that results, b = 4, c = 5, B = 30 degree

Solution

We have....using the Law of Sines.....

sinC / c = sin B / b

sin C / 5 = sin 30 / 4

So.....

sin-1 (5 * sin 30 / 4) = C = about 38.7°

And A= 180 - 30 - 38.7 = 111.3°

So ..to find c, we have

a / sin 111.3 = 4 / sin 30

a = 4sin 111.3 / sin 30 = 7.45

Now to see if we have another triangle...... subtract C from 180

180 - 38.7 = 141.3

Adding this possible angle to B = 141.3 + 30 < 180

So....Another triangle exists

with C = 141.3 B = 30 A = 8.7 b = 4 c= 5

from sine rule a = bsinA/sinB = 8sin8.7 = 1.21