Triangle calculator

Please enter what you know about the triangle:
You have entered side a, c and angle β.

Right scalene triangle.

Sides: a = 32   b = 116.4821758228   c = 112

Area: T = 1792
Perimeter: p = 260.4821758228
Semiperimeter: s = 130.2410879114

Angle ∠ A = α = 15.94553959009° = 15°56'43″ = 0.2788299659 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 74.05546040991° = 74°3'17″ = 1.29224966678 rad

Height: ha = 112
Height: hb = 30.76987663245
Height: hc = 32

Median: ma = 113.137708499
Median: mb = 58.24108791142
Median: mc = 64.49880619864

Inradius: r = 13.75991208858
Circumradius: R = 58.24108791142

Vertex coordinates: A[112; 0] B[0; 0] C[-0; 32]
Centroid: CG[37.33333333333; 10.66766666667]
Coordinates of the circumscribed circle: U[56; 16]
Coordinates of the inscribed circle: I[13.75991208858; 13.75991208858]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.0554604099° = 164°3'17″ = 0.2788299659 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 105.9455395901° = 105°56'43″ = 1.29224966678 rad

How did we calculate this triangle?

1. Input data entered: side a, c and angle β. 2. Calculation of the third side b of the triangle using a Law of Cosines Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS. 3. The triangle circumference is the sum of the lengths of its three sides 4. Semiperimeter of the triangle 5. The triangle area using Heron's formula 6. Calculate the heights of the triangle from its area. 7. Calculation of the inner angles of the triangle using a Law of Cosines     