Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37   b = 34   c = 3.1

Area: T = 13.85499726985
Perimeter: p = 74.1
Semiperimeter: s = 37.05

Angle ∠ A = α = 164.7633265639° = 164°45'48″ = 2.87656614717 rad
Angle ∠ B = β = 13.97550346481° = 13°58'30″ = 0.24439103677 rad
Angle ∠ C = γ = 1.26216997129° = 1°15'42″ = 0.02220208142 rad

Height: ha = 0.74986471729
Height: hb = 0.81547042764
Height: hc = 8.93554662571

Median: ma = 15.51098355891
Median: mb = 20.0087623547
Median: mc = 35.49878520477

Inradius: r = 0.37438184264
Circumradius: R = 70.39436405668

Vertex coordinates: A[3.1; 0] B[0; 0] C[35.90548387097; 8.93554662571]
Centroid: CG[13.00216129032; 2.97884887524]
Coordinates of the circumscribed circle: U[1.55; 70.37765737461]
Coordinates of the inscribed circle: I[3.05; 0.37438184264]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 15.23767343611° = 15°14'12″ = 2.87656614717 rad
∠ B' = β' = 166.0254965352° = 166°1'30″ = 0.24439103677 rad
∠ C' = γ' = 178.7388300287° = 178°44'18″ = 0.02220208142 rad

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How did we calculate this triangle?

a = 37 ; ; b = 34 ; ; c = 3.1 ; ;

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

p = a+b+c = 37+34+3.1 = 74.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74.1 }{ 2 } = 37.05 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.05 * (37.05-37)(37.05-34)(37.05-3.1) } ; ; T = sqrt{ 191.82 } = 13.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.85 }{ 37 } = 0.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.85 }{ 34 } = 0.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.85 }{ 3.1 } = 8.94 ; ;

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{ 34**2+3.1**2-37**2 }{ 2 * 34 * 3.1 } ) = 164° 45'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 37**2+3.1**2-34**2 }{ 2 * 37 * 3.1 } ) = 13° 58'30" ; ; gamma = 180° - alpha - beta = 180° - 164° 45'48" - 13° 58'30" = 1° 15'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.85 }{ 37.05 } = 0.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 37 }{ 2 * sin 164° 45'48" } = 70.39 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 3.1**2 - 37**2 } }{ 2 } = 15.51 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.1**2+2 * 37**2 - 34**2 } }{ 2 } = 20.008 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 34**2+2 * 37**2 - 3.1**2 } }{ 2 } = 35.498 ; ;
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