# 40 50 60 triangle

### Acute scalene triangle.

Sides: a = 40   b = 50   c = 60

Area: T = 992.1576741649
Perimeter: p = 150
Semiperimeter: s = 75

Angle ∠ A = α = 41.41096221093° = 41°24'35″ = 0.72327342478 rad
Angle ∠ B = β = 55.77111336722° = 55°46'16″ = 0.97333899101 rad
Angle ∠ C = γ = 82.81992442185° = 82°49'9″ = 1.44554684956 rad

Height: ha = 49.60878370825
Height: hb = 39.6866269666
Height: hc = 33.07218913883

Median: ma = 51.47881507049
Median: mb = 44.44109720866
Median: mc = 33.91216499156

Inradius: r = 13.22987565553
Circumradius: R = 30.23771578407

Vertex coordinates: A[60; 0] B[0; 0] C[22.5; 33.07218913883]
Centroid: CG[27.5; 11.02439637961]
Coordinates of the circumscribed circle: U[30; 3.78796447301]
Coordinates of the inscribed circle: I[25; 13.22987565553]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5990377891° = 138°35'25″ = 0.72327342478 rad
∠ B' = β' = 124.2298866328° = 124°13'44″ = 0.97333899101 rad
∠ C' = γ' = 97.18107557815° = 97°10'51″ = 1.44554684956 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    