Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 8.39   b = 8.39   c = 4.06

Area: T = 16.5265646374
Perimeter: p = 20.84
Semiperimeter: s = 10.42

Angle ∠ A = α = 75.99880624266° = 75°59'53″ = 1.32664164145 rad
Angle ∠ B = β = 75.99880624266° = 75°59'53″ = 1.32664164145 rad
Angle ∠ C = γ = 28.00438751467° = 28°14″ = 0.48987598246 rad

Height: ha = 3.93993674312
Height: hb = 3.93993674312
Height: hc = 8.14107124995

Median: ma = 5.08332887976
Median: mb = 5.08332887976
Median: mc = 8.14107124995

Inradius: r = 1.58659545465
Circumradius: R = 4.3233460631

Vertex coordinates: A[4.06; 0] B[0; 0] C[2.03; 8.14107124995]
Centroid: CG[2.03; 2.71435708332]
Coordinates of the circumscribed circle: U[2.03; 3.81772518685]
Coordinates of the inscribed circle: I[2.03; 1.58659545465]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 104.0021937573° = 104°7″ = 1.32664164145 rad
∠ B' = β' = 104.0021937573° = 104°7″ = 1.32664164145 rad
∠ C' = γ' = 151.9966124853° = 151°59'46″ = 0.48987598246 rad

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How did we calculate this triangle?

a = 8.39 ; ; b = 8.39 ; ; c = 4.06 ; ;

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

p = a+b+c = 8.39+8.39+4.06 = 20.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.84 }{ 2 } = 10.42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.42 * (10.42-8.39)(10.42-8.39)(10.42-4.06) } ; ; T = sqrt{ 273.1 } = 16.53 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 16.53 }{ 8.39 } = 3.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 16.53 }{ 8.39 } = 3.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 16.53 }{ 4.06 } = 8.14 ; ;

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{ 8.39**2-8.39**2-4.06**2 }{ 2 * 8.39 * 4.06 } ) = 75° 59'53" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.39**2-8.39**2-4.06**2 }{ 2 * 8.39 * 4.06 } ) = 75° 59'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.06**2-8.39**2-8.39**2 }{ 2 * 8.39 * 8.39 } ) = 28° 14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 16.53 }{ 10.42 } = 1.59 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.39 }{ 2 * sin 75° 59'53" } = 4.32 ; ;

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