# 17 24 24 triangle

### Acute isosceles triangle.

Sides: a = 17   b = 24   c = 24

Area: T = 190.7777193343
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 41.4854759909° = 41°29'5″ = 0.72440456498 rad
Angle ∠ B = β = 69.25876200455° = 69°15'27″ = 1.20987735019 rad
Angle ∠ C = γ = 69.25876200455° = 69°15'27″ = 1.20987735019 rad

Height: ha = 22.44443756875
Height: hb = 15.89880994453
Height: hc = 15.89880994453

Median: ma = 22.44443756875
Median: mb = 16.98552877515
Median: mc = 16.98552877515

Inradius: r = 5.87700674875
Circumradius: R = 12.83217224774

Vertex coordinates: A[24; 0] B[0; 0] C[6.02108333333; 15.89880994453]
Centroid: CG[10.00769444444; 5.29993664818]
Coordinates of the circumscribed circle: U[12; 4.54545683774]
Coordinates of the inscribed circle: I[8.5; 5.87700674875]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.5155240091° = 138°30'55″ = 0.72440456498 rad
∠ B' = β' = 110.7422379954° = 110°44'33″ = 1.20987735019 rad
∠ C' = γ' = 110.7422379954° = 110°44'33″ = 1.20987735019 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    