How to find the area of non right triangle

We find area of a non triangle by remembering the three combinations of AreaΔ = ½ ab sin C

Step-by-step explanation:

Can be expressed using the lengths of two sides and the sine of the included angle. AreaΔ = ½ ab sin C.

You may see this referred to as the SAS formula for the area of a triangle.

Where the angle is snug between the two sides and A is the top vertices, we usually enter the the adjacent AB BC lengths then sin. = ½  ac sin B  (left angle) and not AreaΔ = ½ ab sin C. (the right angle)

But when we have the angle at B the left side of the triangle we have to rearrange, and to do this we can make a map and draw the triangle out in bold below.  with equation for AreaΔ = 1/2 ac sin B

                                             A      Top side angle

                      7cm    = c    /        \   b

right side angle  30     B     _     C   left side angle

                                   8cm = a

First we recognize aA  bB and cC is opposite one another. and can ignore the lines AB BC AC and focus on the equations.  

B = 30 degree  BA = 7cm   BC = 8cm

AreaΔ = 1/2 ac sin B  eg) 30 degree angle at point B

a = 8cm c=7cm 1/2 = 8*7 sin 30  = 1/2 56 1/2 = Area ΔABC = 14cmsq^2

Therefore with sin B if given an area we find 14cm  is 1/2 1/2 of 56 the sin.

C = 1/2 cb sin A

or sin a given an area, it will always be the opposite to the ABC vertices A= a(opposite line) B= b (opposite line)and C = c (opposite line)

And that is how you remember how to find the area. The opposite line that is missing for A is the base so if that is missing we do the first equation.

If the right side b line is missing we do the second equation given in the example.

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Step-by-step explanation: