17 17 28 triangle

Obtuse isosceles triangle.

Sides: a = 17   b = 17   c = 28

Area: T = 135.0111110654
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 34.566032178° = 34°33'37″ = 0.60331914056 rad
Angle ∠ B = β = 34.566032178° = 34°33'37″ = 0.60331914056 rad
Angle ∠ C = γ = 110.879935644° = 110°52'46″ = 1.93552098424 rad

Height: ha = 15.88436600769
Height: hb = 15.88436600769
Height: hc = 9.6443650761

Median: ma = 21.54664614264
Median: mb = 21.54664614264
Median: mc = 9.6443650761

Inradius: r = 4.35551971179
Circumradius: R = 14.98439519889

Vertex coordinates: A[28; 0] B[0; 0] C[14; 9.6443650761]
Centroid: CG[14; 3.21545502537]
Coordinates of the circumscribed circle: U[14; -5.34403012279]
Coordinates of the inscribed circle: I[14; 4.35551971179]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.443967822° = 145°26'23″ = 0.60331914056 rad
∠ B' = β' = 145.443967822° = 145°26'23″ = 0.60331914056 rad
∠ C' = γ' = 69.121064356° = 69°7'14″ = 1.93552098424 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 = 17 ; ; b = 17 ; ; c = 28 ; ;

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

p = a+b+c = 17+17+28 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-17)(31-17)(31-28) } ; ; T = sqrt{ 18228 } = 135.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.01 }{ 17 } = 15.88 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.01 }{ 17 } = 15.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.01 }{ 28 } = 9.64 ; ;

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{ 17**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 34° 33'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-17**2-28**2 }{ 2 * 17 * 28 } ) = 34° 33'37" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-17**2-17**2 }{ 2 * 17 * 17 } ) = 110° 52'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.01 }{ 31 } = 4.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 34° 33'37" } = 14.98 ; ;




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