# 5 7 8 triangle

### Acute scalene triangle.

Sides: a = 5   b = 7   c = 8

Area: T = 17.32105080757
Perimeter: p = 20
Semiperimeter: s = 10

Angle ∠ A = α = 38.21332107017° = 38°12'48″ = 0.66769463445 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 81.78767892983° = 81°47'12″ = 1.42774487579 rad

Height: ha = 6.92882032303
Height: hb = 4.94987165931
Height: hc = 4.33301270189

Median: ma = 7.08987234394
Median: mb = 5.67989083458
Median: mc = 4.5832575695

Inradius: r = 1.73220508076
Circumradius: R = 4.04114518843

Vertex coordinates: A[8; 0] B[0; 0] C[2.5; 4.33301270189]
Centroid: CG[3.5; 1.4433375673]
Coordinates of the circumscribed circle: U[4; 0.57773502692]
Coordinates of the inscribed circle: I[3; 1.73220508076]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.7876789298° = 141°47'12″ = 0.66769463445 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 98.21332107017° = 98°12'48″ = 1.42774487579 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.