# 10 21 27 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 21   c = 27

Area: T = 93.89435567544
Perimeter: p = 58
Semiperimeter: s = 29

Angle ∠ A = α = 19.34112748244° = 19°20'29″ = 0.33875689272 rad
Angle ∠ B = β = 44.06876983467° = 44°4'4″ = 0.76991264299 rad
Angle ∠ C = γ = 116.5911026829° = 116°35'28″ = 2.03548972964 rad

Height: ha = 18.77987113509
Height: hb = 8.94222435004
Height: hc = 6.95550782781

Median: ma = 23.66443191324
Median: mb = 17.44327635425
Median: mc = 9.3944147114

Inradius: r = 3.23877088536
Circumradius: R = 15.09768825657

Vertex coordinates: A[27; 0] B[0; 0] C[7.18551851852; 6.95550782781]
Centroid: CG[11.39550617284; 2.3188359426]
Coordinates of the circumscribed circle: U[13.5; -6.75876521961]
Coordinates of the inscribed circle: I[8; 3.23877088536]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.6598725176° = 160°39'31″ = 0.33875689272 rad
∠ B' = β' = 135.9322301653° = 135°55'56″ = 0.76991264299 rad
∠ C' = γ' = 63.40989731711° = 63°24'32″ = 2.03548972964 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    