Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 149   b = 176   c = 27.55

Area: T = 443.4411236946
Perimeter: p = 352.55
Semiperimeter: s = 176.275

Angle ∠ A = α = 10.539916654° = 10°32'21″ = 0.18439431565 rad
Angle ∠ B = β = 167.5232749481° = 167°31'22″ = 2.92438235504 rad
Angle ∠ C = γ = 1.93880839794° = 1°56'17″ = 0.03438259466 rad

Height: ha = 5.95222313684
Height: hb = 5.03991049653
Height: hc = 32.19217413391

Median: ma = 101.5743870902
Median: mb = 61.12328373851
Median: mc = 162.4776919515

Inradius: r = 2.51656218236
Circumradius: R = 407.309943573

Vertex coordinates: A[27.55; 0] B[0; 0] C[-145.4810898367; 32.19217413391]
Centroid: CG[-39.31102994555; 10.73105804464]
Coordinates of the circumscribed circle: U[13.775; 407.0766437306]
Coordinates of the inscribed circle: I[0.275; 2.51656218236]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 169.461083346° = 169°27'39″ = 0.18439431565 rad
∠ B' = β' = 12.47772505193° = 12°28'38″ = 2.92438235504 rad
∠ C' = γ' = 178.0621916021° = 178°3'43″ = 0.03438259466 rad

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How did we calculate this triangle?

a = 149 ; ; b = 176 ; ; c = 27.55 ; ;

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

p = a+b+c = 149+176+27.55 = 352.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 352.55 }{ 2 } = 176.28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 176.28 * (176.28-149)(176.28-176)(176.28-27.55) } ; ; T = sqrt{ 196640.13 } = 443.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 443.44 }{ 149 } = 5.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 443.44 }{ 176 } = 5.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 443.44 }{ 27.55 } = 32.19 ; ;

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{ 176**2+27.55**2-149**2 }{ 2 * 176 * 27.55 } ) = 10° 32'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 149**2+27.55**2-176**2 }{ 2 * 149 * 27.55 } ) = 167° 31'22" ; ; gamma = 180° - alpha - beta = 180° - 10° 32'21" - 167° 31'22" = 1° 56'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 443.44 }{ 176.28 } = 2.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 149 }{ 2 * sin 10° 32'21" } = 407.31 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 176**2+2 * 27.55**2 - 149**2 } }{ 2 } = 101.574 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27.55**2+2 * 149**2 - 176**2 } }{ 2 } = 61.123 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 176**2+2 * 149**2 - 27.55**2 } }{ 2 } = 162.477 ; ;
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