Solve the triangle not a right triangle A 50 degree c 20 d

Solve the triangle (not a right triangle) A = 50 degree, c = 20 degree, a = 3

Solution

Law of sines is:

a / sin(A) = b / sin(B)

Where a and A are opposite side and angle.

You are given the angles A and B and the length a. You can use the law of sines to find the length b:

a / sin(A) = b / sin(B)
3 / sin(50) = b / sin(20)
b sin(50) = 3 sin(20)
b = 2 sin(20) / sin(50)
b = 1.5535

Though you still have a missing c and C to completely solve the triangle.

We know the sum of all three internal angles must equal 180, so we can find C:

A + B + C = 180
50 + 20 + C = 180
70 + C = 180
C = 110

now that we know c, we can use law of sines again to find C:

a / sin(A) = c / sin(C)
3 / sin(50) = c / sin(110)
c sin(50) = 3 sin(110)
c = 3 sin(110) / sin(50)
c = 3.68

So the angles are:

A = 50, B = 20, C = 110

and the lengths are:

a = 3, b = 1.5535, and c = 3.68