How this calculator works
The missing angle A is opposite the known side. Once it is found, the sine rule converts the known side into b and c. Substituting those expressions into the sine area formula gives a direct ASA area equation. The table shows the angle combination and the perpendicular height to the included side.
Formula
A = π - B - C; b = a sin(B)/sin(A); c = a sin(C)/sin(A); K = a² sin(B)sin(C)/(2sin(A)).
Worked example
If a = 10 m and B = C = 45°, A = 90°. Both other sides are √50 m, the area is 25 m² and the height to a is 5 m.
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Frequently asked questions
Where is the included side?
It is the side joining the two known angle vertices. Here those vertices are B and C, so their joining side is called a.
Can B and C total more than 180 degrees?
No. Their sum must be smaller than 180 degrees to leave a positive third angle.
Do I need a second side measurement?
No. One side sets the size and two angles set the shape. Additional measurements can be used to check field data.