Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 34.64   b = 69.28   c = 60

Area: T = 1039.219999866
Perimeter: p = 163.92
Semiperimeter: s = 81.96

Angle ∠ A = α = 309.9999999573° = 30° = 0.52435987749 rad
Angle ∠ B = β = 89.9977088898° = 89°59'50″ = 1.57107455185 rad
Angle ∠ C = γ = 60.00329111447° = 60°10″ = 1.04772483603 rad

Height: ha = 609.9999999226
Height: hb = 309.9999999613
Height: hc = 34.64399999553

Median: ma = 62.44989935868
Median: mb = 34.64215242159
Median: mc = 45.82438365919

Inradius: r = 12.67993557669
Circumradius: R = 34.64400000447

Vertex coordinates: A[60; 0] B[0; 0] C[0.002176; 34.64399999553]
Centroid: CG[20.00105866667; 11.54766666518]
Coordinates of the circumscribed circle: U[30; 17.31884757729]
Coordinates of the inscribed circle: I[12.68; 12.67993557669]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1500.000000043° = 150° = 0.52435987749 rad
∠ B' = β' = 90.0032911102° = 90°10″ = 1.57107455185 rad
∠ C' = γ' = 119.9977088855° = 119°59'50″ = 1.04772483603 rad

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How did we calculate this triangle?

a = 34.64 ; ; b = 69.28 ; ; c = 60 ; ;

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

p = a+b+c = 34.64+69.28+60 = 163.92 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 163.92 }{ 2 } = 81.96 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 81.96 * (81.96-34.64)(81.96-69.28)(81.96-60) } ; ; T = sqrt{ 1079936.64 } = 1039.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1039.2 }{ 34.64 } = 60 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1039.2 }{ 69.28 } = 30 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1039.2 }{ 60 } = 34.64 ; ;

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{ 69.28**2+60**2-34.64**2 }{ 2 * 69.28 * 60 } ) = 30° ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 34.64**2+60**2-69.28**2 }{ 2 * 34.64 * 60 } ) = 89° 59'50" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 34.64**2+69.28**2-60**2 }{ 2 * 34.64 * 69.28 } ) = 60° 10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1039.2 }{ 81.96 } = 12.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 34.64 }{ 2 * sin 30° } = 34.64 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 69.28**2+2 * 60**2 - 34.64**2 } }{ 2 } = 62.449 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 60**2+2 * 34.64**2 - 69.28**2 } }{ 2 } = 34.642 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 69.28**2+2 * 34.64**2 - 60**2 } }{ 2 } = 45.824 ; ;
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