# 17 27 29 triangle

### Acute scalene triangle.

Sides: a = 17   b = 27   c = 29

Area: T = 225.1943666652
Perimeter: p = 73
Semiperimeter: s = 36.5

Angle ∠ A = α = 35.11441523899° = 35°6'51″ = 0.61328575733 rad
Angle ∠ B = β = 66.00326925267° = 66°10″ = 1.15219642998 rad
Angle ∠ C = γ = 78.88331550833° = 78°52'59″ = 1.37767707806 rad

Height: ha = 26.49333725472
Height: hb = 16.68110123446
Height: hc = 15.53105977001

Median: ma = 26.69773781484
Median: mb = 19.56439975465
Median: mc = 17.28443860174

Inradius: r = 6.17696894973
Circumradius: R = 14.77772805935

Vertex coordinates: A[29; 0] B[0; 0] C[6.91437931034; 15.53105977001]
Centroid: CG[11.97112643678; 5.17768659]
Coordinates of the circumscribed circle: U[14.5; 2.84992142321]
Coordinates of the inscribed circle: I[9.5; 6.17696894973]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.886584761° = 144°53'9″ = 0.61328575733 rad
∠ B' = β' = 113.9977307473° = 113°59'50″ = 1.15219642998 rad
∠ C' = γ' = 101.1176844917° = 101°7'1″ = 1.37767707806 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    