10 17 22 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 17   c = 22

Area: T = 81.61545667145
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 25.87770564012° = 25°52'37″ = 0.45216398349 rad
Angle ∠ B = β = 47.89878434641° = 47°53'52″ = 0.83659750731 rad
Angle ∠ C = γ = 106.2255100135° = 106°13'30″ = 1.85439777456 rad

Height: ha = 16.32329133429
Height: hb = 9.60217137311
Height: hc = 7.4219506065

Median: ma = 19.01331533418
Median: mb = 14.82439670804
Median: mc = 8.57332140997

Inradius: r = 3.33112068047
Circumradius: R = 11.45662882294

Vertex coordinates: A[22; 0] B[0; 0] C[6.70545454545; 7.4219506065]
Centroid: CG[9.56881818182; 2.47331686883]
Coordinates of the circumscribed circle: U[11; -3.20110217112]
Coordinates of the inscribed circle: I[7.5; 3.33112068047]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.1232943599° = 154°7'23″ = 0.45216398349 rad
∠ B' = β' = 132.1022156536° = 132°6'8″ = 0.83659750731 rad
∠ C' = γ' = 73.77548998653° = 73°46'30″ = 1.85439777456 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 = 10 ; ; b = 17 ; ; c = 22 ; ;

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

p = a+b+c = 10+17+22 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-10)(24.5-17)(24.5-22) } ; ; T = sqrt{ 6660.94 } = 81.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 81.61 }{ 10 } = 16.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 81.61 }{ 17 } = 9.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 81.61 }{ 22 } = 7.42 ; ;

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{ 10**2-17**2-22**2 }{ 2 * 17 * 22 } ) = 25° 52'37" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-10**2-22**2 }{ 2 * 10 * 22 } ) = 47° 53'52" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-10**2-17**2 }{ 2 * 17 * 10 } ) = 106° 13'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 81.61 }{ 24.5 } = 3.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 25° 52'37" } = 11.46 ; ;




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