Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 7.5   b = 6.2   c = 9.64

Area: T = 23.24658342933
Perimeter: p = 23.34
Semiperimeter: s = 11.67

Angle ∠ A = α = 51.06658661685° = 51°3'57″ = 0.89112675 rad
Angle ∠ B = β = 40.0198752268° = 40°1'7″ = 0.69884589896 rad
Angle ∠ C = γ = 88.91553815635° = 88°54'55″ = 1.55218661639 rad

Height: ha = 6.19988891449
Height: hb = 7.49986562236
Height: hc = 4.82327871978

Median: ma = 7.18548660391
Median: mb = 8.06110049001
Median: mc = 4.91104582271

Inradius: r = 1.99219309591
Circumradius: R = 4.8210863755

Vertex coordinates: A[9.64; 0] B[0; 0] C[5.74437551867; 4.82327871978]
Centroid: CG[5.12879183956; 1.60875957326]
Coordinates of the circumscribed circle: U[4.82; 0.09112542855]
Coordinates of the inscribed circle: I[5.47; 1.99219309591]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.9344133832° = 128°56'3″ = 0.89112675 rad
∠ B' = β' = 139.9811247732° = 139°58'52″ = 0.69884589896 rad
∠ C' = γ' = 91.08546184365° = 91°5'5″ = 1.55218661639 rad

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How did we calculate this triangle?

a = 7.5 ; ; b = 6.2 ; ; c = 9.64 ; ;

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

p = a+b+c = 7.5+6.2+9.64 = 23.34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.34 }{ 2 } = 11.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.67 * (11.67-7.5)(11.67-6.2)(11.67-9.64) } ; ; T = sqrt{ 540.37 } = 23.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 23.25 }{ 7.5 } = 6.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 23.25 }{ 6.2 } = 7.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 23.25 }{ 9.64 } = 4.82 ; ;

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{ 6.2**2+9.64**2-7.5**2 }{ 2 * 6.2 * 9.64 } ) = 51° 3'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.5**2+9.64**2-6.2**2 }{ 2 * 7.5 * 9.64 } ) = 40° 1'7" ; ; gamma = 180° - alpha - beta = 180° - 51° 3'57" - 40° 1'7" = 88° 54'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 23.25 }{ 11.67 } = 1.99 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.5 }{ 2 * sin 51° 3'57" } = 4.82 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.2**2+2 * 9.64**2 - 7.5**2 } }{ 2 } = 7.185 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 9.64**2+2 * 7.5**2 - 6.2**2 } }{ 2 } = 8.061 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.2**2+2 * 7.5**2 - 9.64**2 } }{ 2 } = 4.91 ; ;
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