# 12 15 16 triangle

### Acute scalene triangle.

Sides: a = 12   b = 15   c = 16

Area: T = 85.45113750621
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 45.40656099767° = 45°24'20″ = 0.7922477393 rad
Angle ∠ B = β = 62.88881400862° = 62°53'17″ = 1.0987605105 rad
Angle ∠ C = γ = 71.70662499371° = 71°42'22″ = 1.25215101557 rad

Height: ha = 14.24218958437
Height: hb = 11.39435166749
Height: hc = 10.68114218828

Median: ma = 14.33003496461
Median: mb = 11.99895788083
Median: mc = 10.97772492001

Inradius: r = 3.9744482561
Circumradius: R = 8.42658445166

Vertex coordinates: A[16; 0] B[0; 0] C[5.469875; 10.68114218828]
Centroid: CG[7.156625; 3.56604739609]
Coordinates of the circumscribed circle: U[8; 2.64547789733]
Coordinates of the inscribed circle: I[6.5; 3.9744482561]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.5944390023° = 134°35'40″ = 0.7922477393 rad
∠ B' = β' = 117.1121859914° = 117°6'43″ = 1.0987605105 rad
∠ C' = γ' = 108.2943750063° = 108°17'37″ = 1.25215101557 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.