How this calculator works
First subtract the two supplied angles from 180 degrees. Because one opposite side-angle pair is known, the sine rule supplies both remaining sides. The area follows from two sides and their included angle. Dividing twice that area by each side gives the three perpendicular heights. AAS gives one triangle when the angles are valid and the side is positive.
Formula
C = π - A - B; b = a sin(B)/sin(A); c = a sin(C)/sin(A); K = bc sin(A)/2; h_a = 2K/a.
Worked example
With a = 5 m, A = 30° and B = 60°, C = 90°, b = 5√3 m and c = 10 m. The area is 25√3/2 m² and the height to a is 5√3 m.
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Frequently asked questions
What makes this AAS rather than ASA?
Side a is opposite A. It is not the side connecting the vertices with the two known angles A and B.
Does the ambiguous sine-rule case occur here?
No. The two angles already fix the shape. The ambiguous case belongs to two sides and a non-included angle, called SSA.
Can a height extend outside the triangle?
Yes. For an obtuse triangle some altitudes meet an extension of a side. Their lengths and the area stay positive.