# 10 13 13 triangle

### Acute isosceles triangle.

Sides: a = 10   b = 13   c = 13

Area: T = 60
Perimeter: p = 36
Semiperimeter: s = 18

Angle ∠ A = α = 45.24397298961° = 45°14'23″ = 0.79895822394 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 67.3880135052° = 67°22'49″ = 1.17660052071 rad

Height: ha = 12
Height: hb = 9.23107692308
Height: hc = 9.23107692308

Median: ma = 12
Median: mb = 9.60546863561
Median: mc = 9.60546863561

Inradius: r = 3.33333333333
Circumradius: R = 7.04216666667

Vertex coordinates: A[13; 0] B[0; 0] C[3.84661538462; 9.23107692308]
Centroid: CG[5.61553846154; 3.07769230769]
Coordinates of the circumscribed circle: U[6.5; 2.70883333333]
Coordinates of the inscribed circle: I[5; 3.33333333333]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.7660270104° = 134°45'37″ = 0.79895822394 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 112.6219864948° = 112°37'11″ = 1.17660052071 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.