Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 7.07   b = 4.47   c = 7.07

Area: T = 14.9911115679
Perimeter: p = 18.61
Semiperimeter: s = 9.305

Angle ∠ A = α = 71.57112896572° = 71°34'17″ = 1.24991546544 rad
Angle ∠ B = β = 36.85774206856° = 36°51'27″ = 0.64332833448 rad
Angle ∠ C = γ = 71.57112896572° = 71°34'17″ = 1.24991546544 rad

Height: ha = 4.2410768226
Height: hb = 6.70774343083
Height: hc = 4.2410768226

Median: ma = 4.74220117039
Median: mb = 6.70774343083
Median: mc = 4.74220117039

Inradius: r = 1.61110817495
Circumradius: R = 3.72660819639

Vertex coordinates: A[7.07; 0] B[0; 0] C[5.65769236209; 4.2410768226]
Centroid: CG[4.24223078736; 1.41435894087]
Coordinates of the circumscribed circle: U[3.535; 1.17879056845]
Coordinates of the inscribed circle: I[4.835; 1.61110817495]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108.4298710343° = 108°25'43″ = 1.24991546544 rad
∠ B' = β' = 143.1432579314° = 143°8'33″ = 0.64332833448 rad
∠ C' = γ' = 108.4298710343° = 108°25'43″ = 1.24991546544 rad

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How did we calculate this triangle?

a = 7.07 ; ; b = 4.47 ; ; c = 7.07 ; ;

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

p = a+b+c = 7.07+4.47+7.07 = 18.61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.61 }{ 2 } = 9.31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.31 * (9.31-7.07)(9.31-4.47)(9.31-7.07) } ; ; T = sqrt{ 224.73 } = 14.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.99 }{ 7.07 } = 4.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.99 }{ 4.47 } = 6.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.99 }{ 7.07 } = 4.24 ; ;

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{ 4.47**2+7.07**2-7.07**2 }{ 2 * 4.47 * 7.07 } ) = 71° 34'17" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.07**2+7.07**2-4.47**2 }{ 2 * 7.07 * 7.07 } ) = 36° 51'27" ; ; gamma = 180° - alpha - beta = 180° - 71° 34'17" - 36° 51'27" = 71° 34'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.99 }{ 9.31 } = 1.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.07 }{ 2 * sin 71° 34'17" } = 3.73 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 7.07**2 - 7.07**2 } }{ 2 } = 4.742 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.07**2+2 * 7.07**2 - 4.47**2 } }{ 2 } = 6.707 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.47**2+2 * 7.07**2 - 7.07**2 } }{ 2 } = 4.742 ; ;
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