13 17 17 triangle

Acute isosceles triangle.

Sides: a = 13   b = 17   c = 17

Area: T = 102.1043807471
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 44.95990112188° = 44°57'32″ = 0.78546827742 rad
Angle ∠ B = β = 67.52204943906° = 67°31'14″ = 1.17884549397 rad
Angle ∠ C = γ = 67.52204943906° = 67°31'14″ = 1.17884549397 rad

Height: ha = 15.70882780724
Height: hb = 12.01222126436
Height: hc = 12.01222126436

Median: ma = 15.70882780724
Median: mb = 12.52199840255
Median: mc = 12.52199840255

Inradius: r = 4.34548428711
Circumradius: R = 9.19989713534

Vertex coordinates: A[17; 0] B[0; 0] C[4.97105882353; 12.01222126436]
Centroid: CG[7.32435294118; 4.00440708812]
Coordinates of the circumscribed circle: U[8.5; 3.51772537528]
Coordinates of the inscribed circle: I[6.5; 4.34548428711]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.0410988781° = 135°2'28″ = 0.78546827742 rad
∠ B' = β' = 112.4879505609° = 112°28'46″ = 1.17884549397 rad
∠ C' = γ' = 112.4879505609° = 112°28'46″ = 1.17884549397 rad

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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.

a = 13 ; ; b = 17 ; ; c = 17 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 13+17+17 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-13)(23.5-17)(23.5-17) } ; ; T = sqrt{ 10425.19 } = 102.1 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 102.1 }{ 13 } = 15.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 102.1 }{ 17 } = 12.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 102.1 }{ 17 } = 12.01 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 13**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 44° 57'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-13**2-17**2 }{ 2 * 13 * 17 } ) = 67° 31'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 17**2-13**2-17**2 }{ 2 * 17 * 13 } ) = 67° 31'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 102.1 }{ 23.5 } = 4.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 13 }{ 2 * sin 44° 57'32" } = 9.2 ; ;




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