# 13 15 16 triangle

### Acute scalene triangle.

Sides: a = 13   b = 15   c = 16

Area: T = 91.19221049214
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 49.45883981265° = 49°27'30″ = 0.86332118901 rad
Angle ∠ B = β = 61.26443462551° = 61°15'52″ = 1.06992645562 rad
Angle ∠ C = γ = 69.27772556184° = 69°16'38″ = 1.20991162073 rad

Height: ha = 14.03295546033
Height: hb = 12.15989473229
Height: hc = 11.39990131152

Median: ma = 14.08801278403
Median: mb = 12.5
Median: mc = 11.53325625947

Inradius: r = 4.14550956782
Circumradius: R = 8.55333720345

Vertex coordinates: A[16; 0] B[0; 0] C[6.25; 11.39990131152]
Centroid: CG[7.41766666667; 3.87996710384]
Coordinates of the circumscribed circle: U[8; 3.02765777968]
Coordinates of the inscribed circle: I[7; 4.14550956782]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.5421601874° = 130°32'30″ = 0.86332118901 rad
∠ B' = β' = 118.7365653745° = 118°44'8″ = 1.06992645562 rad
∠ C' = γ' = 110.7232744382° = 110°43'22″ = 1.20991162073 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    