# 10 16 23 triangle

### Obtuse scalene triangle.

Sides: a = 10   b = 16   c = 23

Area: T = 67.30110958306
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 21.45547820505° = 21°27'17″ = 0.37444565871 rad
Angle ∠ B = β = 35.8199022505° = 35°49'8″ = 0.62551598776 rad
Angle ∠ C = γ = 122.7266195444° = 122°43'34″ = 2.1421976189 rad

Height: ha = 13.46602191661
Height: hb = 8.41326369788
Height: hc = 5.85222692027

Median: ma = 19.17702895127
Median: mb = 15.82771917913
Median: mc = 6.76438746292

Inradius: r = 2.74769835033
Circumradius: R = 13.67699111455

Vertex coordinates: A[23; 0] B[0; 0] C[8.10986956522; 5.85222692027]
Centroid: CG[10.37695652174; 1.95107564009]
Coordinates of the circumscribed circle: U[11.5; -7.3990295713]
Coordinates of the inscribed circle: I[8.5; 2.74769835033]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.545521795° = 158°32'43″ = 0.37444565871 rad
∠ B' = β' = 144.1810977495° = 144°10'52″ = 0.62551598776 rad
∠ C' = γ' = 57.27438045555° = 57°16'26″ = 2.1421976189 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    