Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 37   b = 34   c = 3.6

Area: T = 35.2776619736
Perimeter: p = 74.6
Semiperimeter: s = 37.3

Angle ∠ A = α = 144.8011189247° = 144°48'4″ = 2.52772575132 rad
Angle ∠ B = β = 31.98437670296° = 31°59'2″ = 0.55882220419 rad
Angle ∠ C = γ = 3.21550437236° = 3°12'54″ = 0.05661130986 rad

Height: ha = 1.90768443101
Height: hb = 2.07550952786
Height: hc = 19.59881220756

Median: ma = 15.56437399104
Median: mb = 20.04994388949
Median: mc = 35.48660535986

Inradius: r = 0.94657538803
Circumradius: R = 32.09549118275

Vertex coordinates: A[3.6; 0] B[0; 0] C[31.38333333333; 19.59881220756]
Centroid: CG[11.66111111111; 6.53327073585]
Coordinates of the circumscribed circle: U[1.8; 32.04443967834]
Coordinates of the inscribed circle: I[3.3; 0.94657538803]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 35.19988107532° = 35°11'56″ = 2.52772575132 rad
∠ B' = β' = 148.016623297° = 148°58″ = 0.55882220419 rad
∠ C' = γ' = 176.7854956276° = 176°47'6″ = 0.05661130986 rad

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How did we calculate this triangle?

a = 37 ; ; b = 34 ; ; c = 3.6 ; ;

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

p = a+b+c = 37+34+3.6 = 74.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 74.6 }{ 2 } = 37.3 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.3 * (37.3-37)(37.3-34)(37.3-3.6) } ; ; T = sqrt{ 1244.44 } = 35.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.28 }{ 37 } = 1.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.28 }{ 34 } = 2.08 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.28 }{ 3.6 } = 19.6 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 37**2-34**2-3.6**2 }{ 2 * 34 * 3.6 } ) = 144° 48'4" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 34**2-37**2-3.6**2 }{ 2 * 37 * 3.6 } ) = 31° 59'2" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.6**2-37**2-34**2 }{ 2 * 34 * 37 } ) = 3° 12'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.28 }{ 37.3 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 37 }{ 2 * sin 144° 48'4" } = 32.09 ; ;




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