Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 1200   b = 1700   c = 1348.37

Area: T = 803771.0621696
Perimeter: p = 4248.37
Semiperimeter: s = 2124.185

Angle ∠ A = α = 44.53114639787° = 44°31'53″ = 0.77772206672 rad
Angle ∠ B = β = 83.46985275345° = 83°28'7″ = 1.45768006273 rad
Angle ∠ C = γ = 522.0000084868° = 52° = 0.90875713592 rad

Height: ha = 1339.618843616
Height: hb = 945.6133013761
Height: hc = 1192.211142816

Median: ma = 1412.109864612
Median: mb = 952.1329627966
Median: mc = 1307.851113288

Inradius: r = 378.3990329325
Circumradius: R = 855.5532946318

Vertex coordinates: A[1348.37; 0] B[0; 0] C[136.499875661; 1192.211142816]
Centroid: CG[494.9566252203; 397.4043809388]
Coordinates of the circumscribed circle: U[674.185; 526.7310889287]
Coordinates of the inscribed circle: I[424.185; 378.3990329325]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.4698536021° = 135°28'7″ = 0.77772206672 rad
∠ B' = β' = 96.53114724655° = 96°31'53″ = 1.45768006273 rad
∠ C' = γ' = 1287.999991513° = 128° = 0.90875713592 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 = 1200+1700+1348.37 = 4248.37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 4248.37 }{ 2 } = 2124.19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2124.19 * (2124.19-1200)(2124.19-1700)(2124.19-1348.37) } ; ; T = sqrt{ 646047919621 } = 803771.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 803771.06 }{ 1200 } = 1339.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 803771.06 }{ 1700 } = 945.61 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 803771.06 }{ 1348.37 } = 1192.21 ; ;

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{ 1700**2+1348.37**2-1200**2 }{ 2 * 1700 * 1348.37 } ) = 44° 31'53" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1200**2+1348.37**2-1700**2 }{ 2 * 1200 * 1348.37 } ) = 83° 28'7" ; ; gamma = 180° - alpha - beta = 180° - 44° 31'53" - 83° 28'7" = 52° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 803771.06 }{ 2124.19 } = 378.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1200 }{ 2 * sin 44° 31'53" } = 855.55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1700**2+2 * 1348.37**2 - 1200**2 } }{ 2 } = 1412.109 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1348.37**2+2 * 1200**2 - 1700**2 } }{ 2 } = 952.13 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1700**2+2 * 1200**2 - 1348.37**2 } }{ 2 } = 1307.851 ; ;
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