Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 7.07   b = 7.07   c = 6.32

Area: T = 19.98554199375
Perimeter: p = 20.46
Semiperimeter: s = 10.23

Angle ∠ A = α = 63.45112578791° = 63°27'5″ = 1.10774333645 rad
Angle ∠ B = β = 63.45112578791° = 63°27'5″ = 1.10774333645 rad
Angle ∠ C = γ = 53.09774842418° = 53°5'51″ = 0.92767259245 rad

Height: ha = 5.65435841407
Height: hb = 5.65435841407
Height: hc = 6.32444999802

Median: ma = 5.69880193927
Median: mb = 5.69880193927
Median: mc = 6.32444999802

Inradius: r = 1.95436089871
Circumradius: R = 3.95216878928

Vertex coordinates: A[6.32; 0] B[0; 0] C[3.16; 6.32444999802]
Centroid: CG[3.16; 2.10881666601]
Coordinates of the circumscribed circle: U[3.16; 2.37328120874]
Coordinates of the inscribed circle: I[3.16; 1.95436089871]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.5498742121° = 116°32'55″ = 1.10774333645 rad
∠ B' = β' = 116.5498742121° = 116°32'55″ = 1.10774333645 rad
∠ C' = γ' = 126.9032515758° = 126°54'9″ = 0.92767259245 rad

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How did we calculate this triangle?

a = 7.07 ; ; b = 7.07 ; ; c = 6.32 ; ;

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

p = a+b+c = 7.07+7.07+6.32 = 20.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 20.46 }{ 2 } = 10.23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.23 * (10.23-7.07)(10.23-7.07)(10.23-6.32) } ; ; T = sqrt{ 399.42 } = 19.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19.99 }{ 7.07 } = 5.65 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19.99 }{ 7.07 } = 5.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19.99 }{ 6.32 } = 6.32 ; ;

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{ 7.07**2+6.32**2-7.07**2 }{ 2 * 7.07 * 6.32 } ) = 63° 27'5" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.07**2+6.32**2-7.07**2 }{ 2 * 7.07 * 6.32 } ) = 63° 27'5" ; ; gamma = 180° - alpha - beta = 180° - 63° 27'5" - 63° 27'5" = 53° 5'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19.99 }{ 10.23 } = 1.95 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.07 }{ 2 * sin 63° 27'5" } = 3.95 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 6.32**2 - 7.07**2 } }{ 2 } = 5.698 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 7.07**2 - 7.07**2 } }{ 2 } = 5.698 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 7.07**2 - 6.32**2 } }{ 2 } = 6.324 ; ;
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