Triangle calculator SSS - result

Acute isosceles triangle.

Sides: a = 6.32 b = 7.07 c = 7.07

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

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

Height: h_a = 6.32444999802
Height: h_b = 5.65435841407
Height: h_c = 5.65435841407

Median: m_a = 6.32444999802
Median: m_b = 5.69880193927
Median: m_c = 5.69880193927

Inradius: r = 1.95436089871
Circumradius: R = 3.95216878928

Vertex coordinates: A[7.07; 0] B[0; 0] C[2.82547807638; 5.65435841407]
Centroid: CG[3.29882602546; 1.88545280469]
Coordinates of the circumscribed circle: U[3.535; 1.76662423962]
Coordinates of the inscribed circle: I[3.16; 1.95436089871]

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

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How did we calculate this triangle?

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

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

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

2. Semiperimeter of the triangle

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

3. The triangle area using Heron's formula

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

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

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

5. Calculation of the inner angles of the triangle using a Law of Cosines

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

6. Inradius

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

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.32 }{ 2 * sin 53° 5'51" } = 3.95 ; ;$

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