100.3 75.9 90.2 triangle

Acute scalene triangle.

Sides: a = 100.3   b = 75.9   c = 90.2

Area: T = 3285.955491326
Perimeter: p = 266.4
Semiperimeter: s = 133.2

Angle ∠ A = α = 73.72771576732° = 73°43'38″ = 1.28767816495 rad
Angle ∠ B = β = 46.58765922002° = 46°35'12″ = 0.81330894212 rad
Angle ∠ C = γ = 59.68662501266° = 59°41'11″ = 1.04217215829 rad

Height: ha = 65.52325306732
Height: hb = 86.5866427227
Height: hc = 72.85993107154

Median: ma = 66.58438005824
Median: mb = 87.50992138006
Median: mc = 76.65879415325

Inradius: r = 24.66993311807
Circumradius: R = 52.24329455155

Vertex coordinates: A[90.2; 0] B[0; 0] C[68.93219290466; 72.85993107154]
Centroid: CG[53.04439763489; 24.28664369051]
Coordinates of the circumscribed circle: U[45.1; 26.36988330446]
Coordinates of the inscribed circle: I[57.3; 24.66993311807]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 106.2732842327° = 106°16'22″ = 1.28767816495 rad
∠ B' = β' = 133.41334078° = 133°24'48″ = 0.81330894212 rad
∠ C' = γ' = 120.3143749873° = 120°18'49″ = 1.04217215829 rad

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How did we calculate this triangle?

a = 100.3 ; ; b = 75.9 ; ; c = 90.2 ; ;

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

p = a+b+c = 100.3+75.9+90.2 = 266.4 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 266.4 }{ 2 } = 133.2 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 133.2 * (133.2-100.3)(133.2-75.9)(133.2-90.2) } ; ; T = sqrt{ 10797499.69 } = 3285.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3285.95 }{ 100.3 } = 65.52 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3285.95 }{ 75.9 } = 86.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3285.95 }{ 90.2 } = 72.86 ; ;

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{ 100.3**2-75.9**2-90.2**2 }{ 2 * 75.9 * 90.2 } ) = 73° 43'38" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 75.9**2-100.3**2-90.2**2 }{ 2 * 100.3 * 90.2 } ) = 46° 35'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 90.2**2-100.3**2-75.9**2 }{ 2 * 75.9 * 100.3 } ) = 59° 41'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3285.95 }{ 133.2 } = 24.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 100.3 }{ 2 * sin 73° 43'38" } = 52.24 ; ;




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