Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3.4   b = 3.19   c = 4.8

Area: T = 5.41331940016
Perimeter: p = 11.39
Semiperimeter: s = 5.695

Angle ∠ A = α = 44.99656024997° = 44°59'44″ = 0.78553214125 rad
Angle ∠ B = β = 41.55882869951° = 41°33'30″ = 0.72553289396 rad
Angle ∠ C = γ = 93.44661105052° = 93°26'46″ = 1.63109423015 rad

Height: ha = 3.18442317657
Height: hb = 3.39438520386
Height: hc = 2.25554975007

Median: ma = 3.70437886009
Median: mb = 3.84113506739
Median: mc = 2.26600995553

Inradius: r = 0.9510516945
Circumradius: R = 2.40443475989

Vertex coordinates: A[4.8; 0] B[0; 0] C[2.544415625; 2.25554975007]
Centroid: CG[2.44880520833; 0.75218325002]
Coordinates of the circumscribed circle: U[2.4; -0.14545246558]
Coordinates of the inscribed circle: I[2.505; 0.9510516945]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 135.00443975° = 135°16″ = 0.78553214125 rad
∠ B' = β' = 138.4421713005° = 138°26'30″ = 0.72553289396 rad
∠ C' = γ' = 86.55438894948° = 86°33'14″ = 1.63109423015 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 = 3.4+3.19+4.8 = 11.39 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 11.39 }{ 2 } = 5.7 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 5.7 * (5.7-3.4)(5.7-3.19)(5.7-4.8) } ; ; T = sqrt{ 29.3 } = 5.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 5.41 }{ 3.4 } = 3.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 5.41 }{ 3.19 } = 3.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 5.41 }{ 4.8 } = 2.26 ; ;

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{ 3.19**2+4.8**2-3.4**2 }{ 2 * 3.19 * 4.8 } ) = 44° 59'44" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.4**2+4.8**2-3.19**2 }{ 2 * 3.4 * 4.8 } ) = 41° 33'30" ; ;
 gamma = 180° - alpha - beta = 180° - 44° 59'44" - 41° 33'30" = 93° 26'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 5.41 }{ 5.7 } = 0.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.4 }{ 2 * sin 44° 59'44" } = 2.4 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.19**2+2 * 4.8**2 - 3.4**2 } }{ 2 } = 3.704 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.8**2+2 * 3.4**2 - 3.19**2 } }{ 2 } = 3.841 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.19**2+2 * 3.4**2 - 4.8**2 } }{ 2 } = 2.26 ; ;
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