# 4 15 15 triangle

### Acute isosceles triangle.

Sides: a = 4   b = 15   c = 15

Area: T = 29.73221374946
Perimeter: p = 34
Semiperimeter: s = 17

Angle ∠ A = α = 15.32545113215° = 15°19'28″ = 0.26774631788 rad
Angle ∠ B = β = 82.33877443392° = 82°20'16″ = 1.43770647374 rad
Angle ∠ C = γ = 82.33877443392° = 82°20'16″ = 1.43770647374 rad

Height: ha = 14.86660687473
Height: hb = 3.96442849993
Height: hc = 3.96442849993

Median: ma = 14.86660687473
Median: mb = 8.01656097709
Median: mc = 8.01656097709

Inradius: r = 1.74989492644
Circumradius: R = 7.56875689325

Vertex coordinates: A[15; 0] B[0; 0] C[0.53333333333; 3.96442849993]
Centroid: CG[5.17877777778; 1.32114283331]
Coordinates of the circumscribed circle: U[7.5; 1.0099009191]
Coordinates of the inscribed circle: I[2; 1.74989492644]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6755488678° = 164°40'32″ = 0.26774631788 rad
∠ B' = β' = 97.66222556608° = 97°39'44″ = 1.43770647374 rad
∠ C' = γ' = 97.66222556608° = 97°39'44″ = 1.43770647374 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    