# 16 29 30 triangle

### Acute scalene triangle.

Sides: a = 16   b = 29   c = 30

Area: T = 226.7122235003
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 31.41112725322° = 31°24'41″ = 0.54882301279 rad
Angle ∠ B = β = 70.84549899264° = 70°50'42″ = 1.23664783328 rad
Angle ∠ C = γ = 77.74437375414° = 77°44'37″ = 1.35768841929 rad

Height: ha = 28.33990293754
Height: hb = 15.63553265519
Height: hc = 15.11441490002

Median: ma = 28.39989436423
Median: mb = 19.17768089108
Median: mc = 17.98661057486

Inradius: r = 6.04656596001
Circumradius: R = 15.3549855291

Vertex coordinates: A[30; 0] B[0; 0] C[5.25; 15.11441490002]
Centroid: CG[11.75; 5.03880496667]
Coordinates of the circumscribed circle: U[15; 3.25985360909]
Coordinates of the inscribed circle: I[8.5; 6.04656596001]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.5898727468° = 148°35'19″ = 0.54882301279 rad
∠ B' = β' = 109.1555010074° = 109°9'18″ = 1.23664783328 rad
∠ C' = γ' = 102.2566262459° = 102°15'23″ = 1.35768841929 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    