70 67 82 triangle

Acute scalene triangle.

Sides: a = 70   b = 67   c = 82

Area: T = 2248.363294612
Perimeter: p = 219
Semiperimeter: s = 109.5

Angle ∠ A = α = 54.93328655241° = 54°55'58″ = 0.9598759371 rad
Angle ∠ B = β = 51.57330979085° = 51°34'23″ = 0.9900120364 rad
Angle ∠ C = γ = 73.49440365675° = 73°29'39″ = 1.28327129187 rad

Height: ha = 64.23989413178
Height: hb = 67.11553118246
Height: hc = 54.83881206372

Median: ma = 66.19328999214
Median: mb = 68.48217493935
Median: mc = 54.89553549948

Inradius: r = 20.53329949418
Circumradius: R = 42.76222240287

Vertex coordinates: A[82; 0] B[0; 0] C[43.5066097561; 54.83881206372]
Centroid: CG[41.83553658537; 18.27993735457]
Coordinates of the circumscribed circle: U[41; 12.14993952065]
Coordinates of the inscribed circle: I[42.5; 20.53329949418]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 125.0677134476° = 125°4'2″ = 0.9598759371 rad
∠ B' = β' = 128.4276902092° = 128°25'37″ = 0.9900120364 rad
∠ C' = γ' = 106.5065963433° = 106°30'21″ = 1.28327129187 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 = 70 ; ; b = 67 ; ; c = 82 ; ;

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

p = a+b+c = 70+67+82 = 219 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 219 }{ 2 } = 109.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 109.5 * (109.5-70)(109.5-67)(109.5-82) } ; ; T = sqrt{ 5055135.94 } = 2248.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2248.36 }{ 70 } = 64.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2248.36 }{ 67 } = 67.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2248.36 }{ 82 } = 54.84 ; ;

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{ 70**2-67**2-82**2 }{ 2 * 67 * 82 } ) = 54° 55'58" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 67**2-70**2-82**2 }{ 2 * 70 * 82 } ) = 51° 34'23" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 82**2-70**2-67**2 }{ 2 * 67 * 70 } ) = 73° 29'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2248.36 }{ 109.5 } = 20.53 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 70 }{ 2 * sin 54° 55'58" } = 42.76 ; ;




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