# 10 30 30 triangle

### Acute isosceles triangle.

Sides: a = 10   b = 30   c = 30

Area: T = 147.9021994578
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 80.40659317731° = 80°24'21″ = 1.40333482476 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 29.58803989155
Height: hb = 9.86601329718
Height: hc = 9.86601329718

Median: ma = 29.58803989155
Median: mb = 16.58331239518
Median: mc = 16.58331239518

Inradius: r = 4.22657712736
Circumradius: R = 15.21327765851

Vertex coordinates: A[30; 0] B[0; 0] C[1.66766666667; 9.86601329718]
Centroid: CG[10.55655555556; 3.28767109906]
Coordinates of the circumscribed circle: U[15; 2.53554627642]
Coordinates of the inscribed circle: I[5; 4.22657712736]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 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    