# 12 17 21 triangle

### Obtuse scalene triangle.

Sides: a = 12   b = 17   c = 21

Area: T = 101.9880390272
Perimeter: p = 50
Semiperimeter: s = 25

Angle ∠ A = α = 34.84222349066° = 34°50'32″ = 0.60881117179 rad
Angle ∠ B = β = 54.03442464357° = 54°2'3″ = 0.94330755091 rad
Angle ∠ C = γ = 91.12435186577° = 91°7'25″ = 1.59904054266 rad

Height: ha = 16.9976731712
Height: hb = 11.99876929732
Height: hc = 9.71224181211

Median: ma = 18.13883571472
Median: mb = 14.84108220797
Median: mc = 10.3087764064

Inradius: r = 4.07992156109
Circumradius: R = 10.50220190366

Vertex coordinates: A[21; 0] B[0; 0] C[7.04876190476; 9.71224181211]
Centroid: CG[9.34992063492; 3.2377472707]
Coordinates of the circumscribed circle: U[10.5; -0.20659219419]
Coordinates of the inscribed circle: I[8; 4.07992156109]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.1587765093° = 145°9'28″ = 0.60881117179 rad
∠ B' = β' = 125.9665753564° = 125°57'57″ = 0.94330755091 rad
∠ C' = γ' = 88.87664813423° = 88°52'35″ = 1.59904054266 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    