Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 200   b = 234   c = 71.01

Area: T = 6672.863286727
Perimeter: p = 505.01
Semiperimeter: s = 252.505

Angle ∠ A = α = 53.43437741614° = 53°26'2″ = 0.93325952909 rad
Angle ∠ B = β = 109.9987509389° = 109°59'51″ = 1.92198187078 rad
Angle ∠ C = γ = 16.56987164492° = 16°34'7″ = 0.28991786549 rad

Height: ha = 66.72986286727
Height: hb = 57.03330159596
Height: hc = 187.9411497459

Median: ma = 141.0654559865
Median: mb = 93.98798385293
Median: mc = 214.7549609953

Inradius: r = 26.42766563722
Circumradius: R = 124.5076829606

Vertex coordinates: A[71.01; 0] B[0; 0] C[-68.39658590339; 187.9411497459]
Centroid: CG[0.8711380322; 62.64771658196]
Coordinates of the circumscribed circle: U[35.505; 119.3377109038]
Coordinates of the inscribed circle: I[18.505; 26.42766563722]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 126.5666225839° = 126°33'58″ = 0.93325952909 rad
∠ B' = β' = 70.00224906106° = 70°9″ = 1.92198187078 rad
∠ C' = γ' = 163.4311283551° = 163°25'53″ = 0.28991786549 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 = 200+234+71.01 = 505.01 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 505.01 }{ 2 } = 252.51 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 252.51 * (252.51-200)(252.51-234)(252.51-71.01) } ; ; T = sqrt{ 44527098.85 } = 6672.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6672.86 }{ 200 } = 66.73 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6672.86 }{ 234 } = 57.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6672.86 }{ 71.01 } = 187.94 ; ;

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{ 234**2+71.01**2-200**2 }{ 2 * 234 * 71.01 } ) = 53° 26'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 200**2+71.01**2-234**2 }{ 2 * 200 * 71.01 } ) = 109° 59'51" ; ; gamma = 180° - alpha - beta = 180° - 53° 26'2" - 109° 59'51" = 16° 34'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6672.86 }{ 252.51 } = 26.43 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 200 }{ 2 * sin 53° 26'2" } = 124.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 234**2+2 * 71.01**2 - 200**2 } }{ 2 } = 141.065 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 71.01**2+2 * 200**2 - 234**2 } }{ 2 } = 93.98 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 234**2+2 * 200**2 - 71.01**2 } }{ 2 } = 214.75 ; ;
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