# 8 21 27 triangle

### Obtuse scalene triangle.

Sides: a = 8   b = 21   c = 27

Area: T = 62.610990337
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 12.75987404169° = 12°45'31″ = 0.22326820287 rad
Angle ∠ B = β = 35.43109446873° = 35°25'51″ = 0.61883866419 rad
Angle ∠ C = γ = 131.8110314896° = 131°48'37″ = 2.3010523983 rad

Height: ha = 15.65224758425
Height: hb = 5.963284794
Height: hc = 4.638777062

Median: ma = 23.85437208838
Median: mb = 16.91989243157
Median: mc = 8.38215273071

Inradius: r = 2.23660679775
Circumradius: R = 18.11221506177

Vertex coordinates: A[27; 0] B[0; 0] C[6.51985185185; 4.638777062]
Centroid: CG[11.17328395062; 1.546592354]
Coordinates of the circumscribed circle: U[13.5; -12.07547670785]
Coordinates of the inscribed circle: I[7; 2.23660679775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 167.2411259583° = 167°14'29″ = 0.22326820287 rad
∠ B' = β' = 144.5699055313° = 144°34'9″ = 0.61883866419 rad
∠ C' = γ' = 48.19896851042° = 48°11'23″ = 2.3010523983 rad

# How did we calculate this triangle?

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. ### 1. The triangle circumference is the sum of the lengths of its three sides ### 2. Semiperimeter of the triangle ### 3. The triangle area using Heron's formula ### 4. Calculate the heights of the triangle from its area. ### 5. Calculation of the inner angles of the triangle using a Law of Cosines    