Triangle calculator

You have entered side a, b and angle α.

Right scalene triangle.

Sides: a = 85   b = 45   c = 72.11110255093

Area: T = 1622.498807396
Perimeter: p = 202.1111025509
Semiperimeter: s = 101.0565512755

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 31.96657187508° = 31°57'57″ = 0.558790704 rad
Angle ∠ C = γ = 58.03442812492° = 58°2'3″ = 1.01328892868 rad

Height: ha = 38.17664252696
Height: hb = 72.11110255093
Height: hc = 45

Median: ma = 42.5
Median: mb = 75.54397246487
Median: mc = 57.66328129734

Vertex coordinates: A[72.11110255093; 0] B[0; 0] C[72.11110255093; 45]
Centroid: CG[48.07440170062; 15]
Coordinates of the circumscribed circle: U[36.05655127546; 22.5]
Coordinates of the inscribed circle: I[56.05655127546; 16.05655127546]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 148.0344281249° = 148°2'3″ = 0.558790704 rad
∠ C' = γ' = 121.9665718751° = 121°57'57″ = 1.01328892868 rad

How did we calculate this triangle?

1. Input data entered: side a, b and angle α. 2. From angle α, side b and side a we calculate side c - by using the law of cosines and quadratic equation: 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    