# 10 10 17 triangle

### Obtuse isosceles triangle.

Sides: a = 10   b = 10   c = 17

Area: T = 44.77765284496
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ B = β = 31.78883306171° = 31°47'18″ = 0.5554811033 rad
Angle ∠ C = γ = 116.4233338766° = 116°25'24″ = 2.03219705876 rad

Height: ha = 8.95553056899
Height: hb = 8.95553056899
Height: hc = 5.26878268764

Median: ma = 13.01992165663
Median: mb = 13.01992165663
Median: mc = 5.26878268764

Inradius: r = 2.42203528892
Circumradius: R = 9.49215799575

Vertex coordinates: A[17; 0] B[0; 0] C[8.5; 5.26878268764]
Centroid: CG[8.5; 1.75659422921]
Coordinates of the circumscribed circle: U[8.5; -4.22437530811]
Coordinates of the inscribed circle: I[8.5; 2.42203528892]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ B' = β' = 148.2121669383° = 148°12'42″ = 0.5554811033 rad
∠ C' = γ' = 63.57766612341° = 63°34'36″ = 2.03219705876 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    