Triangle calculator SSS - result

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Acute scalene triangle.

Sides: a = 7.5   b = 5.3   c = 6.7

Area: T = 17.25553388477
Perimeter: p = 19.5
Semiperimeter: s = 9.75

Angle ∠ A = α = 76.37549258882° = 76°22'30″ = 1.33329939227 rad
Angle ∠ B = β = 43.37657282066° = 43°22'33″ = 0.75770492727 rad
Angle ∠ C = γ = 60.24993459052° = 60°14'58″ = 1.05215494582 rad

Height: ha = 4.60114236927
Height: hb = 6.51114486218
Height: hc = 5.15108474172

Median: ma = 4.73657681531
Median: mb = 6.59990529624
Median: mc = 5.56330477258

Inradius: r = 1.77697783434
Circumradius: R = 3.85985883817

Vertex coordinates: A[6.7; 0] B[0; 0] C[5.45114925373; 5.15108474172]
Centroid: CG[4.05504975124; 1.71769491391]
Coordinates of the circumscribed circle: U[3.35; 1.915473348]
Coordinates of the inscribed circle: I[4.45; 1.77697783434]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 103.6255074112° = 103°37'30″ = 1.33329939227 rad
∠ B' = β' = 136.6244271793° = 136°37'27″ = 0.75770492727 rad
∠ C' = γ' = 119.7510654095° = 119°45'2″ = 1.05215494582 rad

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How did we calculate this triangle?

a = 7.5 ; ; b = 5.3 ; ; c = 6.7 ; ;

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

p = a+b+c = 7.5+5.3+6.7 = 19.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19.5 }{ 2 } = 9.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.75 * (9.75-7.5)(9.75-5.3)(9.75-6.7) } ; ; T = sqrt{ 297.75 } = 17.26 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 17.26 }{ 7.5 } = 4.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 17.26 }{ 5.3 } = 6.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 17.26 }{ 6.7 } = 5.15 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 5.3**2+6.7**2-7.5**2 }{ 2 * 5.3 * 6.7 } ) = 76° 22'30" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.5**2+6.7**2-5.3**2 }{ 2 * 7.5 * 6.7 } ) = 43° 22'33" ; ; gamma = 180° - alpha - beta = 180° - 76° 22'30" - 43° 22'33" = 60° 14'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 17.26 }{ 9.75 } = 1.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.5 }{ 2 * sin 76° 22'30" } = 3.86 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.3**2+2 * 6.7**2 - 7.5**2 } }{ 2 } = 4.736 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.7**2+2 * 7.5**2 - 5.3**2 } }{ 2 } = 6.599 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.3**2+2 * 7.5**2 - 6.7**2 } }{ 2 } = 5.563 ; ;
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