# 5 5 7 triangle

### Acute isosceles triangle.

Sides: a = 5   b = 5   c = 7

Area: T = 12.497749975
Perimeter: p = 17
Semiperimeter: s = 8.5

Angle ∠ A = α = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ B = β = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ C = γ = 88.85440080016° = 88°51'14″ = 1.55107949932 rad

Height: ha = 4.99989999
Height: hb = 4.99989999
Height: hc = 3.57107142143

Median: ma = 5.54552682532
Median: mb = 5.54552682532
Median: mc = 3.57107142143

Inradius: r = 1.47702940882
Circumradius: R = 3.50107002101

Vertex coordinates: A[7; 0] B[0; 0] C[3.5; 3.57107142143]
Centroid: CG[3.5; 1.19902380714]
Coordinates of the circumscribed circle: U[3.5; 0.07700140042]
Coordinates of the inscribed circle: I[3.5; 1.47702940882]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ B' = β' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ C' = γ' = 91.14659919984° = 91°8'46″ = 1.55107949932 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    