# 7 17 18 triangle

### Acute scalene triangle.

Sides: a = 7   b = 17   c = 18

Area: T = 59.39769696197
Perimeter: p = 42
Semiperimeter: s = 21

Angle ∠ A = α = 22.84435073179° = 22°50'37″ = 0.39986944154 rad
Angle ∠ B = β = 70.52987793655° = 70°31'44″ = 1.23109594173 rad
Angle ∠ C = γ = 86.62877133166° = 86°37'40″ = 1.51219388208 rad

Height: ha = 16.97105627485
Height: hb = 6.98878787788
Height: hc = 6.65996632911

Median: ma = 17.15437167984
Median: mb = 10.68987791632
Median: mc = 9.38108315196

Inradius: r = 2.82884271247
Circumradius: R = 9.01656114601

Vertex coordinates: A[18; 0] B[0; 0] C[2.33333333333; 6.65996632911]
Centroid: CG[6.77877777778; 2.21998877637]
Coordinates of the circumscribed circle: U[9; 0.53303300859]
Coordinates of the inscribed circle: I[4; 2.82884271247]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.1566492682° = 157°9'23″ = 0.39986944154 rad
∠ B' = β' = 109.4711220634° = 109°28'16″ = 1.23109594173 rad
∠ C' = γ' = 93.37222866834° = 93°22'20″ = 1.51219388208 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    