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.
