Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, c and angle α.

Acute scalene triangle.

Sides: a = 7.9   b = 8.71223093636   c = 5.8

Area: T = 22.35495550283
Perimeter: p = 22.41223093636
Semiperimeter: s = 11.20661546818

Angle ∠ A = α = 62.2° = 62°12' = 1.08655947947 rad
Angle ∠ B = β = 77.30106669355° = 77°18'2″ = 1.3499151152 rad
Angle ∠ C = γ = 40.49993330645° = 40°29'58″ = 0.70768467068 rad

Height: ha = 5.6588115197
Height: hb = 5.13105696562
Height: hc = 7.70767431132

Median: ma = 6.25985675057
Median: mb = 5.39897046662
Median: mc = 7.79440469092

Inradius: r = 1.99444000117
Circumradius: R = 4.46553910842

Vertex coordinates: A[5.8; 0] B[0; 0] C[1.73766953063; 7.70767431132]
Centroid: CG[2.51222317688; 2.56989143711]
Coordinates of the circumscribed circle: U[2.9; 3.3965543776]
Coordinates of the inscribed circle: I[2.49438453182; 1.99444000117]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 117.8° = 117°48' = 1.08655947947 rad
∠ B' = β' = 102.6999333065° = 102°41'58″ = 1.3499151152 rad
∠ C' = γ' = 139.5010666935° = 139°30'2″ = 0.70768467068 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 = 7.9 ; ; b = 8.71 ; ; c = 5.8 ; ;

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

p = a+b+c = 7.9+8.71+5.8 = 22.41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.41 }{ 2 } = 11.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.21 * (11.21-7.9)(11.21-8.71)(11.21-5.8) } ; ; T = sqrt{ 499.5 } = 22.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22.35 }{ 7.9 } = 5.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22.35 }{ 8.71 } = 5.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22.35 }{ 5.8 } = 7.71 ; ;

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{ 7.9**2-8.71**2-5.8**2 }{ 2 * 8.71 * 5.8 } ) = 62° 12' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.71**2-7.9**2-5.8**2 }{ 2 * 7.9 * 5.8 } ) = 77° 18'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.8**2-7.9**2-8.71**2 }{ 2 * 8.71 * 7.9 } ) = 40° 29'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22.35 }{ 11.21 } = 1.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7.9 }{ 2 * sin 62° 12' } = 4.47 ; ;




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