Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 80   b = 90   c = 120.42

Area: T = 36009.99999172
Perimeter: p = 290.42
Semiperimeter: s = 145.21

Angle ∠ A = α = 41.63218245826° = 41°37'55″ = 0.72766124126 rad
Angle ∠ B = β = 48.36442904453° = 48°21'51″ = 0.84441161087 rad
Angle ∠ C = γ = 90.00438849722° = 90°14″ = 1.57108641324 rad

Height: ha = 909.9999997931
Height: hb = 809.9999998161
Height: hc = 59.7910732299

Median: ma = 98.49110564468
Median: mb = 91.79904581098
Median: mc = 60.20659457197

Inradius: r = 24.79216809567
Circumradius: R = 60.21100001384

Vertex coordinates: A[120.42; 0] B[0; 0] C[53.15113718651; 59.7910732299]
Centroid: CG[57.8577123955; 19.93302440997]
Coordinates of the circumscribed circle: U[60.21; -0.00440825725]
Coordinates of the inscribed circle: I[55.21; 24.79216809567]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.3688175417° = 138°22'5″ = 0.72766124126 rad
∠ B' = β' = 131.6365709555° = 131°38'9″ = 0.84441161087 rad
∠ C' = γ' = 89.99661150278° = 89°59'46″ = 1.57108641324 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 = 80+90+120.42 = 290.42 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 290.42 }{ 2 } = 145.21 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 145.21 * (145.21-80)(145.21-90)(145.21-120.42) } ; ; T = sqrt{ 12959999.94 } = 3600 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3600 }{ 80 } = 90 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3600 }{ 90 } = 80 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3600 }{ 120.42 } = 59.79 ; ;

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{ 90**2+120.42**2-80**2 }{ 2 * 90 * 120.42 } ) = 41° 37'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 80**2+120.42**2-90**2 }{ 2 * 80 * 120.42 } ) = 48° 21'51" ; ; gamma = 180° - alpha - beta = 180° - 41° 37'55" - 48° 21'51" = 90° 14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3600 }{ 145.21 } = 24.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 80 }{ 2 * sin 41° 37'55" } = 60.21 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 120.42**2 - 80**2 } }{ 2 } = 98.491 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 120.42**2+2 * 80**2 - 90**2 } }{ 2 } = 91.79 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 80**2 - 120.42**2 } }{ 2 } = 60.206 ; ;
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