# 13 16 24 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 16   c = 24

Area: T = 96.90768496031
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 30.31329778294° = 30°18'47″ = 0.52990612692 rad
Angle ∠ B = β = 38.40436536582° = 38°24'13″ = 0.67702702011 rad
Angle ∠ C = γ = 111.2833368512° = 111°17' = 1.94222611833 rad

Height: ha = 14.90987460928
Height: hb = 12.11333562004
Height: hc = 8.07655708003

Median: ma = 19.33326149292
Median: mb = 17.56441680703
Median: mc = 8.27664726786

Inradius: r = 3.65768622492
Circumradius: R = 12.87883466299

Vertex coordinates: A[24; 0] B[0; 0] C[10.18875; 8.07655708003]
Centroid: CG[11.39658333333; 2.69218569334]
Coordinates of the circumscribed circle: U[12; -4.67545921661]
Coordinates of the inscribed circle: I[10.5; 3.65768622492]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.6877022171° = 149°41'13″ = 0.52990612692 rad
∠ B' = β' = 141.5966346342° = 141°35'47″ = 0.67702702011 rad
∠ C' = γ' = 68.71766314876° = 68°43' = 1.94222611833 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    