Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 42   b = 33   c = 15.9

Area: T = 240.1821697354
Perimeter: p = 90.9
Semiperimeter: s = 45.45

Angle ∠ A = α = 113.7233018408° = 113°43'23″ = 1.98548411065 rad
Angle ∠ B = β = 45.99985519834° = 45°59'55″ = 0.80328261833 rad
Angle ∠ C = γ = 20.27884296084° = 20°16'42″ = 0.35439253638 rad

Height: ha = 11.43772236835
Height: hb = 14.55664665063
Height: hc = 30.21215342583

Median: ma = 15.16326185074
Median: mb = 27.132217647
Median: mc = 36.92328587734

Inradius: r = 5.28545257944
Circumradius: R = 22.93882590793

Vertex coordinates: A[15.9; 0] B[0; 0] C[29.17664150943; 30.21215342583]
Centroid: CG[15.02554716981; 10.07105114194]
Coordinates of the circumscribed circle: U[7.95; 21.51765338656]
Coordinates of the inscribed circle: I[12.45; 5.28545257944]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 66.27769815918° = 66°16'37″ = 1.98548411065 rad
∠ B' = β' = 134.0011448017° = 134°5″ = 0.80328261833 rad
∠ C' = γ' = 159.7221570392° = 159°43'18″ = 0.35439253638 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+33+15.9 = 90.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 90.9 }{ 2 } = 45.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 45.45 * (45.45-42)(45.45-33)(45.45-15.9) } ; ; T = sqrt{ 57687.25 } = 240.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 240.18 }{ 42 } = 11.44 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 240.18 }{ 33 } = 14.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 240.18 }{ 15.9 } = 30.21 ; ;

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{ 33**2+15.9**2-42**2 }{ 2 * 33 * 15.9 } ) = 113° 43'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 42**2+15.9**2-33**2 }{ 2 * 42 * 15.9 } ) = 45° 59'55" ; ;
 gamma = 180° - alpha - beta = 180° - 113° 43'23" - 45° 59'55" = 20° 16'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 240.18 }{ 45.45 } = 5.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 42 }{ 2 * sin 113° 43'23" } = 22.94 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 15.9**2 - 42**2 } }{ 2 } = 15.163 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.9**2+2 * 42**2 - 33**2 } }{ 2 } = 27.132 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 33**2+2 * 42**2 - 15.9**2 } }{ 2 } = 36.923 ; ;
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