# 8 27 28 triangle

### Acute scalene triangle.

Sides: a = 8   b = 27   c = 28

Area: T = 107.9776559956
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 16.59878421359° = 16°35'52″ = 0.2989686994 rad
Angle ∠ B = β = 74.59659063013° = 74°35'45″ = 1.30219441735 rad
Angle ∠ C = γ = 88.80662515629° = 88°48'23″ = 1.55499614861 rad

Height: ha = 26.99441399891
Height: hb = 7.99882637005
Height: hc = 7.71326114255

Median: ma = 27.21221296484
Median: mb = 15.54883118055
Median: mc = 14.16598022585

Inradius: r = 3.42878273002
Circumradius: R = 14.00330391838

Vertex coordinates: A[28; 0] B[0; 0] C[2.125; 7.71326114255]
Centroid: CG[10.04216666667; 2.57108704752]
Coordinates of the circumscribed circle: U[14; 0.2921729983]
Coordinates of the inscribed circle: I[4.5; 3.42878273002]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.4022157864° = 163°24'8″ = 0.2989686994 rad
∠ B' = β' = 105.4044093699° = 105°24'15″ = 1.30219441735 rad
∠ C' = γ' = 91.19437484371° = 91°11'37″ = 1.55499614861 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    