Triangle calculator

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

Acute scalene triangle.

Sides: a = 10.1   b = 13.76999844563   c = 9.8

Area: T = 49.4222175675
Perimeter: p = 33.65999844563
Semiperimeter: s = 16.87999922281

Angle ∠ A = α = 47.41101317895° = 47°24'36″ = 0.82774628985 rad
Angle ∠ B = β = 87° = 1.51884364492 rad
Angle ∠ C = γ = 45.59898682105° = 45°35'24″ = 0.79656933058 rad

Height: ha = 9.78765694406
Height: hb = 7.21549243428
Height: hc = 10.0866158301

Median: ma = 10.78771352569
Median: mb = 7.21882135238
Median: mc = 10.9932715181

Inradius: r = 2.9421797532
Circumradius: R = 6.85993927876

Vertex coordinates: A[9.8; 0] B[0; 0] C[0.52985931581; 10.0866158301]
Centroid: CG[3.4432864386; 3.3622052767]
Coordinates of the circumscribed circle: U[4.9; 4.88001322288]
Coordinates of the inscribed circle: I[3.11000077719; 2.9421797532]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.598986821° = 132°35'24″ = 0.82774628985 rad
∠ B' = β' = 93° = 1.51884364492 rad
∠ C' = γ' = 134.411013179° = 134°24'36″ = 0.79656933058 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     