Geometry
Area from two sides and the included angle
The base-and-height formula with the height replaced by b x sin C. The angle must be the one between the two known sides.
The Formula
A = 1/2 x a x b x sin C
The base-and-height formula with the height replaced by b x sin C. The angle must be the one between the two known sides.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| a | First known side | length | Treated as the base. |
| b | Second known side | length | Multiplied by sin C to give the height onto side a. |
| C | Angle between sides a and b | degrees | The area is greatest when this angle is 90 degrees. |
What Each Symbol Means
alength
First known side
Treated as the base.
blength
Second known side
Multiplied by sin C to give the height onto side a.
Cdegrees
Angle between sides a and b
The area is greatest when this angle is 90 degrees.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate the area of a triangle page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate The Area Of A Triangle, filed under Math. Every number the guide produces comes from substituting into this one line.