67 78 101 triangle

Acute scalene triangle.

Sides: a = 67   b = 78   c = 101

Area: T = 2611.34444813
Perimeter: p = 246
Semiperimeter: s = 123

Angle ∠ A = α = 41.52549440439° = 41°31'30″ = 0.72547469953 rad
Angle ∠ B = β = 50.51547165407° = 50°30'53″ = 0.88216481243 rad
Angle ∠ C = γ = 87.96603394154° = 87°57'37″ = 1.5355197534 rad

Height: ha = 77.95105815313
Height: hb = 66.95875508025
Height: hc = 51.71097917089

Median: ma = 83.78769321553
Median: mb = 76.31551361134
Median: mc = 52.30991770151

Inradius: r = 21.23304429374
Circumradius: R = 50.53220155748

Vertex coordinates: A[101; 0] B[0; 0] C[42.6043960396; 51.71097917089]
Centroid: CG[47.86879867987; 17.23765972363]
Coordinates of the circumscribed circle: U[50.5; 1.79884988322]
Coordinates of the inscribed circle: I[45; 21.23304429374]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.4755055956° = 138°28'30″ = 0.72547469953 rad
∠ B' = β' = 129.4855283459° = 129°29'7″ = 0.88216481243 rad
∠ C' = γ' = 92.04396605846° = 92°2'23″ = 1.5355197534 rad

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How did we calculate this triangle?

a = 67 ; ; b = 78 ; ; c = 101 ; ;

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

p = a+b+c = 67+78+101 = 246 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 246 }{ 2 } = 123 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 123 * (123-67)(123-78)(123-101) } ; ; T = sqrt{ 6819120 } = 2611.34 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2611.34 }{ 67 } = 77.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2611.34 }{ 78 } = 66.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2611.34 }{ 101 } = 51.71 ; ;

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{ 67**2-78**2-101**2 }{ 2 * 78 * 101 } ) = 41° 31'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 78**2-67**2-101**2 }{ 2 * 67 * 101 } ) = 50° 30'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 101**2-67**2-78**2 }{ 2 * 78 * 67 } ) = 87° 57'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2611.34 }{ 123 } = 21.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 67 }{ 2 * sin 41° 31'30" } = 50.53 ; ;




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