Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 175   b = 168   c = 7.47

Area: T = 223.5770401071
Perimeter: p = 350.47
Semiperimeter: s = 175.235

Angle ∠ A = α = 159.1276931221° = 159°7'37″ = 2.77772888784 rad
Angle ∠ B = β = 20.00216310726° = 20°6″ = 0.3499094318 rad
Angle ∠ C = γ = 0.87114377068° = 0°52'17″ = 0.01552094572 rad

Height: ha = 2.5555090298
Height: hb = 2.66215523937
Height: hc = 59.85882064447

Median: ma = 80.52111180374
Median: mb = 91.01986818736
Median: mc = 171.4955043004

Inradius: r = 1.2765831889
Circumradius: R = 245.5880361877

Vertex coordinates: A[7.47; 0] B[0; 0] C[164.4454504685; 59.85882064447]
Centroid: CG[57.30548348951; 19.95327354816]
Coordinates of the circumscribed circle: U[3.735; 245.5521957668]
Coordinates of the inscribed circle: I[7.235; 1.2765831889]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 20.87330687794° = 20°52'23″ = 2.77772888784 rad
∠ B' = β' = 159.9988368927° = 159°59'54″ = 0.3499094318 rad
∠ C' = γ' = 179.1298562293° = 179°7'43″ = 0.01552094572 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 = 175+168+7.47 = 350.47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 350.47 }{ 2 } = 175.24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 175.24 * (175.24-175)(175.24-168)(175.24-7.47) } ; ; T = sqrt{ 49983.72 } = 223.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 223.57 }{ 175 } = 2.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 223.57 }{ 168 } = 2.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 223.57 }{ 7.47 } = 59.86 ; ;

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{ 168**2+7.47**2-175**2 }{ 2 * 168 * 7.47 } ) = 159° 7'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 175**2+7.47**2-168**2 }{ 2 * 175 * 7.47 } ) = 20° 6" ; ; gamma = 180° - alpha - beta = 180° - 159° 7'37" - 20° 6" = 0° 52'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 223.57 }{ 175.24 } = 1.28 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 175 }{ 2 * sin 159° 7'37" } = 245.58 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 168**2+2 * 7.47**2 - 175**2 } }{ 2 } = 80.521 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.47**2+2 * 175**2 - 168**2 } }{ 2 } = 91.019 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 168**2+2 * 175**2 - 7.47**2 } }{ 2 } = 171.495 ; ;
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