# 12 23 24 triangle

### Acute scalene triangle.

Sides: a = 12   b = 23   c = 24

Area: T = 135.8532631554
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 29.48765793699° = 29°29'12″ = 0.51546378952 rad
Angle ∠ B = β = 70.63442509213° = 70°38'3″ = 1.23328002433 rad
Angle ∠ C = γ = 79.87991697087° = 79°52'45″ = 1.39441545152 rad

Height: ha = 22.64221052589
Height: hb = 11.8133272309
Height: hc = 11.32110526295

Median: ma = 22.72766363547
Median: mb = 15.09113882728
Median: mc = 13.87444369255

Inradius: r = 4.6055173951
Circumradius: R = 12.19896792213

Vertex coordinates: A[24; 0] B[0; 0] C[3.97991666667; 11.32110526295]
Centroid: CG[9.32663888889; 3.77436842098]
Coordinates of the circumscribed circle: U[12; 2.14220269646]
Coordinates of the inscribed circle: I[6.5; 4.6055173951]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150.513342063° = 150°30'48″ = 0.51546378952 rad
∠ B' = β' = 109.3665749079° = 109°21'57″ = 1.23328002433 rad
∠ C' = γ' = 100.1210830291° = 100°7'15″ = 1.39441545152 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.