# 8 9 10 triangle

### Acute scalene triangle.

Sides: a = 8   b = 9   c = 10

Area: T = 34.19770393455
Perimeter: p = 27
Semiperimeter: s = 13.5

Angle ∠ A = α = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ B = β = 58.75215587378° = 58°45'6″ = 1.02554081407 rad
Angle ∠ C = γ = 71.79900431357° = 71°47'24″ = 1.25329726229 rad

Height: ha = 8.54992598364
Height: hb = 7.59993420768
Height: hc = 6.83994078691

Median: ma = 8.63113382508
Median: mb = 7.85881168228
Median: mc = 6.8922024376

Inradius: r = 2.53331140256
Circumradius: R = 5.26436135597

Vertex coordinates: A[10; 0] B[0; 0] C[4.15; 6.83994078691]
Centroid: CG[4.71766666667; 2.2879802623]
Coordinates of the circumscribed circle: U[5; 1.64548792374]
Coordinates of the inscribed circle: I[4.5; 2.53331140256]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ B' = β' = 121.2488441262° = 121°14'54″ = 1.02554081407 rad
∠ C' = γ' = 108.2109956864° = 108°12'36″ = 1.25329726229 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    