How do I find the other side and 2 angles of a triangle that is a Side-Side-Angle case?

Question

The triangle is not a right triangle so SOH CAH TOA won't work. Is there a special trig function that I can/should use?

Answer 1

Draw a line from the point where the two sides you do know perpendicular to the side you don't know. Now use SOH CAH TOA to figure out the pieces that you need.

You can figure out the length of the new line you just drew by using SOH, and you know the angle that you created (180 - 90 - your angle). Then you have CAH for the other triangle.

Answer 2

Use the cosine rule:
a^2 = b^2 + c^2 - 2bc cosA
b^2 = a^2 + c^2 - 2ac cosB
c^2 = a^2 + b^2 - 2ab cosC
Where:
a, b and c are the lenght of the triangle sides and A, B and C are the angles opposite a, b and c respectively.

Answer 3

Use the sine law to solve one of the angles:
sinA / a = sinB / b = sinC / c

Where a is the side opposite angle A, b opposite B and c opposite C.

Use the sum of the interior angles to solve for the other angle:
C = 180 - A - B

Use the cosine law to solve the other side:
c^2 = a^2 + b^2 - 2*a*b*cosC