Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 42   b = 30.04   c = 34.19

Area: T = 507.7532564256
Perimeter: p = 106.23
Semiperimeter: s = 53.115

Angle ∠ A = α = 81.39545868029° = 81°23'41″ = 1.4210603533 rad
Angle ∠ B = β = 45.00664292841° = 45°23″ = 0.78655103756 rad
Angle ∠ C = γ = 53.5998983913° = 53°35'56″ = 0.9355478745 rad

Height: ha = 24.1798693536
Height: hb = 33.80550974871
Height: hc = 29.70218171545

Median: ma = 24.38660380136
Median: mb = 35.22660933116
Median: mc = 32.26439392356

Inradius: r = 9.55994947615
Circumradius: R = 21.23991045544

Vertex coordinates: A[34.19; 0] B[0; 0] C[29.69551520913; 29.70218171545]
Centroid: CG[21.29550506971; 9.90106057182]
Coordinates of the circumscribed circle: U[17.095; 12.60439889429]
Coordinates of the inscribed circle: I[23.075; 9.55994947615]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 98.60554131971° = 98°36'19″ = 1.4210603533 rad
∠ B' = β' = 134.9943570716° = 134°59'37″ = 0.78655103756 rad
∠ C' = γ' = 126.4011016087° = 126°24'4″ = 0.9355478745 rad

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How did we calculate this triangle?

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

p = a+b+c = 42+30.04+34.19 = 106.23 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 106.23 }{ 2 } = 53.12 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 53.12 * (53.12-42)(53.12-30.04)(53.12-34.19) } ; ; T = sqrt{ 257812.67 } = 507.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 507.75 }{ 42 } = 24.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 507.75 }{ 30.04 } = 33.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 507.75 }{ 34.19 } = 29.7 ; ;

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{ 30.04**2+34.19**2-42**2 }{ 2 * 30.04 * 34.19 } ) = 81° 23'41" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 42**2+34.19**2-30.04**2 }{ 2 * 42 * 34.19 } ) = 45° 23" ; ; gamma = 180° - alpha - beta = 180° - 81° 23'41" - 45° 23" = 53° 35'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 507.75 }{ 53.12 } = 9.56 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 42 }{ 2 * sin 81° 23'41" } = 21.24 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.04**2+2 * 34.19**2 - 42**2 } }{ 2 } = 24.386 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 34.19**2+2 * 42**2 - 30.04**2 } }{ 2 } = 35.226 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 30.04**2+2 * 42**2 - 34.19**2 } }{ 2 } = 32.264 ; ;
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