# 9 12 13 triangle

### Acute scalene triangle.

Sides: a = 9   b = 12   c = 13

Area: T = 52.15436192416
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 41.96218888284° = 41°57'43″ = 0.73223731204 rad
Angle ∠ B = β = 63.06442249308° = 63°3'51″ = 1.10106783653 rad
Angle ∠ C = γ = 74.97438862409° = 74°58'26″ = 1.30985411679 rad

Height: ha = 11.59896931648
Height: hb = 8.69222698736
Height: hc = 8.02436337295

Median: ma = 11.67326175299
Median: mb = 9.43439811321
Median: mc = 8.38215273071

Inradius: r = 3.06878599554
Circumradius: R = 6.73301177771

Vertex coordinates: A[13; 0] B[0; 0] C[4.07769230769; 8.02436337295]
Centroid: CG[5.69223076923; 2.67545445765]
Coordinates of the circumscribed circle: U[6.5; 1.74548453496]
Coordinates of the inscribed circle: I[5; 3.06878599554]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0388111172° = 138°2'17″ = 0.73223731204 rad
∠ B' = β' = 116.9365775069° = 116°56'9″ = 1.10106783653 rad
∠ C' = γ' = 105.0266113759° = 105°1'34″ = 1.30985411679 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.