# 40 70 100 triangle

### Obtuse scalene triangle.

Sides: a = 40   b = 70   c = 100

Area: T = 1092.875464972
Perimeter: p = 210
Semiperimeter: s = 105

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 33.12329402077° = 33°7'23″ = 0.57881043646 rad
Angle ∠ C = γ = 128.6822187453° = 128°40'56″ = 2.24659278597 rad

Height: ha = 54.6443732486
Height: hb = 31.2254989992
Height: hc = 21.85774929944

Median: ma = 83.96442781187
Median: mb = 67.63987462923
Median: mc = 27.38661278753

Vertex coordinates: A[100; 0] B[0; 0] C[33.5; 21.85774929944]
Centroid: CG[44.5; 7.28658309981]
Coordinates of the circumscribed circle: U[50; -40.03220384513]
Coordinates of the inscribed circle: I[35; 10.40883299973]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 146.8777059792° = 146°52'37″ = 0.57881043646 rad
∠ C' = γ' = 51.31878125465° = 51°19'4″ = 2.24659278597 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    