# 4 5 6 triangle

### Acute scalene triangle.

Sides: a = 4   b = 5   c = 6

Area: T = 9.92215674165
Perimeter: p = 15
Semiperimeter: s = 7.5

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 = 4.96107837082
Height: hb = 3.96986269666
Height: hc = 3.30771891388

Median: ma = 5.14878150705
Median: mb = 4.44440972087
Median: mc = 3.39111649916

Inradius: r = 1.32328756555
Circumradius: R = 3.02437157841

Vertex coordinates: A[6; 0] B[0; 0] C[2.25; 3.30771891388]
Centroid: CG[2.75; 1.10223963796]
Coordinates of the circumscribed circle: U[3; 0.3787964473]
Coordinates of the inscribed circle: I[2.5; 1.32328756555]

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 ### 6. Inradius ### 7. Circumradius ### 8. Calculation of medians #### Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.