Solve a right triangle from two independent side, acute-angle or altitude measurements, including ambiguous solutions.
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Use the same length unit for every side. A is opposite a; B is opposite b. Two angles do not determine the triangle size.
Hypotenuse c
5
Leg a3
Leg b4
Angle A36.86989765°
Angle B53.13010235°
Altitude to c2.4
Area (square units)6
Perimeter12
How this was calculated
a² + b² = c²; area = ab/2; h = ab/c.
sin(A) = a/c; A + B = 90°.
Formula and method
Let a and b be legs, c the hypotenuse, A the angle opposite a and h the altitude to c. Use a²+b²=c², sin(A)=a/c, cos(A)=b/c and h=ab/c. One side with an acute angle fixes the scale and shape.
Worked example
Legs 3 and 4 give hypotenuse 5 and altitude 12/5 = 2.4. With only c = 5 and h = 2.4, either (a,b) = (3,4) or (4,3) works; the calculator displays both assignments.
Inputs and limitations
Two angles alone cannot determine side lengths. Acute angles must be strictly between 0° and 90°. An altitude to the hypotenuse cannot exceed c/2. The figure labels the sides and angles but is not drawn to scale.
Last updated . Results are estimates for informational purposes only.