3 6 7 triangle

Obtuse scalene triangle.

Sides: a = 3   b = 6   c = 7

Area: T = 8.944427191
Perimeter: p = 16
Semiperimeter: s = 8

Angle ∠ A = α = 25.20987652968° = 25°12'32″ = 0.44399759548 rad
Angle ∠ B = β = 58.41218644948° = 58°24'43″ = 1.01994793577 rad
Angle ∠ C = γ = 96.37993702084° = 96°22'46″ = 1.68221373411 rad

Height: ha = 5.963284794
Height: hb = 2.981142397
Height: hc = 2.556550626

Median: ma = 6.34442887702
Median: mb = 4.4722135955
Median: mc = 3.20215621187

Inradius: r = 1.11880339887
Circumradius: R = 3.52218070646

Vertex coordinates: A[7; 0] B[0; 0] C[1.57114285714; 2.556550626]
Centroid: CG[2.85771428571; 0.852183542]
Coordinates of the circumscribed circle: U[3.5; -0.39113118961]
Coordinates of the inscribed circle: I[2; 1.11880339887]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.7911234703° = 154°47'28″ = 0.44399759548 rad
∠ B' = β' = 121.5888135505° = 121°35'17″ = 1.01994793577 rad
∠ C' = γ' = 83.62106297916° = 83°37'14″ = 1.68221373411 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 = 3 ; ; b = 6 ; ; c = 7 ; ;

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

p = a+b+c = 3+6+7 = 16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16 }{ 2 } = 8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8 * (8-3)(8-6)(8-7) } ; ; T = sqrt{ 80 } = 8.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.94 }{ 3 } = 5.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.94 }{ 6 } = 2.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.94 }{ 7 } = 2.56 ; ;

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{ 3**2-6**2-7**2 }{ 2 * 6 * 7 } ) = 25° 12'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6**2-3**2-7**2 }{ 2 * 3 * 7 } ) = 58° 24'43" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7**2-3**2-6**2 }{ 2 * 6 * 3 } ) = 96° 22'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.94 }{ 8 } = 1.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3 }{ 2 * sin 25° 12'32" } = 3.52 ; ;




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