Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles
°
°

Acute scalene triangle.

Sides: a = 10.42548001625   b = 9.89327413194   c = 8.8

Area: T = 40.21546853917
Perimeter: p = 29.11875414819
Semiperimeter: s = 14.55987707409

Angle ∠ A = α = 67.5° = 67°30' = 1.17880972451 rad
Angle ∠ B = β = 61.25° = 61°15' = 1.06990141668 rad
Angle ∠ C = γ = 51.25° = 51°15' = 0.89444812416 rad

Height: ha = 7.71551954502
Height: hb = 8.13301398861
Height: hc = 9.14397012254

Median: ma = 7.7777149272
Median: mb = 8.28220073962
Median: mc = 9.16603162948

Inradius: r = 2.76222308303
Circumradius: R = 5.64218611928

Vertex coordinates: A[8.8; 0] B[0; 0] C[5.01442117964; 9.14397012254]
Centroid: CG[4.60547372655; 3.04765670751]
Coordinates of the circumscribed circle: U[4.4; 3.53113733474]
Coordinates of the inscribed circle: I[4.66660294216; 2.76222308303]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.5° = 112°30' = 1.17880972451 rad
∠ B' = β' = 118.75° = 118°45' = 1.06990141668 rad
∠ C' = γ' = 128.75° = 128°45' = 0.89444812416 rad

How did we calculate this triangle?

1. Calculate the third unknown inner angle 2. By using the law of sines, we calculate unknown side a 3. By using the law of sines, we calculate last unknown side b 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. 4. The triangle circumference is the sum of the lengths of its three sides 5. Semiperimeter of the triangle 6. The triangle area using Heron's formula 7. Calculate the heights of the triangle from its area. 8. Calculation of the inner angles of the triangle using a Law of Cosines     