# 13 15 20 triangle

### Obtuse scalene triangle.

Sides: a = 13   b = 15   c = 20

Area: T = 97.48884608556
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 40.53658021113° = 40°32'9″ = 0.70774832118 rad
Angle ∠ B = β = 48.58326895819° = 48°34'58″ = 0.84879278927 rad
Angle ∠ C = γ = 90.88215083068° = 90°52'53″ = 1.58661815491 rad

Height: ha = 14.9988224747
Height: hb = 12.99884614474
Height: hc = 9.74988460856

Median: ma = 16.43992822228
Median: mb = 15.10879449297
Median: mc = 9.84988578018

Inradius: r = 4.06220192023
Circumradius: R = 10.00111836421

Vertex coordinates: A[20; 0] B[0; 0] C[8.6; 9.74988460856]
Centroid: CG[9.53333333333; 3.25496153619]
Coordinates of the circumscribed circle: U[10; -0.15438643637]
Coordinates of the inscribed circle: I[9; 4.06220192023]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.4644197889° = 139°27'51″ = 0.70774832118 rad
∠ B' = β' = 131.4177310418° = 131°25'2″ = 0.84879278927 rad
∠ C' = γ' = 89.11884916932° = 89°7'7″ = 1.58661815491 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    