# 15 30 30 triangle

### Acute isosceles triangle.

Sides: a = 15   b = 30   c = 30

Area: T = 217.8555313224
Perimeter: p = 75
Semiperimeter: s = 37.5

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 75.52224878141° = 75°31'21″ = 1.31881160717 rad
Angle ∠ C = γ = 75.52224878141° = 75°31'21″ = 1.31881160717 rad

Height: ha = 29.04773750966
Height: hb = 14.52436875483
Height: hc = 14.52436875483

Median: ma = 29.04773750966
Median: mb = 18.37111730709
Median: mc = 18.37111730709

Inradius: r = 5.80994750193
Circumradius: R = 15.49219333848

Vertex coordinates: A[30; 0] B[0; 0] C[3.75; 14.52436875483]
Centroid: CG[11.25; 4.84112291828]
Coordinates of the circumscribed circle: U[15; 3.87329833462]
Coordinates of the inscribed circle: I[7.5; 5.80994750193]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 104.4787512186° = 104°28'39″ = 1.31881160717 rad
∠ C' = γ' = 104.4787512186° = 104°28'39″ = 1.31881160717 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    