# Triangle calculator ASA - result

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    