Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 66.18   b = 66.18   c = 25.82

Area: T = 837.9769821739
Perimeter: p = 158.18
Semiperimeter: s = 79.09

Angle ∠ A = α = 78.75109511367° = 78°45'3″ = 1.37444633864 rad
Angle ∠ B = β = 78.75109511367° = 78°45'3″ = 1.37444633864 rad
Angle ∠ C = γ = 22.49880977266° = 22°29'53″ = 0.39326658808 rad

Height: ha = 25.32439595569
Height: hb = 25.32439595569
Height: hc = 64.90985841781

Median: ma = 37.79326487561
Median: mb = 37.79326487561
Median: mc = 64.90985841781

Inradius: r = 10.59551425179
Circumradius: R = 33.73881600251

Vertex coordinates: A[25.82; 0] B[0; 0] C[12.91; 64.90985841781]
Centroid: CG[12.91; 21.6366194726]
Coordinates of the circumscribed circle: U[12.91; 31.1770424153]
Coordinates of the inscribed circle: I[12.91; 10.59551425179]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.2499048863° = 101°14'57″ = 1.37444633864 rad
∠ B' = β' = 101.2499048863° = 101°14'57″ = 1.37444633864 rad
∠ C' = γ' = 157.5021902273° = 157°30'7″ = 0.39326658808 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 = 66.18+66.18+25.82 = 158.18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 158.18 }{ 2 } = 79.09 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 79.09 * (79.09-66.18)(79.09-66.18)(79.09-25.82) } ; ; T = sqrt{ 702193.42 } = 837.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 837.97 }{ 66.18 } = 25.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 837.97 }{ 66.18 } = 25.32 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 837.97 }{ 25.82 } = 64.91 ; ;

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{ 66.18**2+25.82**2-66.18**2 }{ 2 * 66.18 * 25.82 } ) = 78° 45'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 66.18**2+25.82**2-66.18**2 }{ 2 * 66.18 * 25.82 } ) = 78° 45'3" ; ; gamma = 180° - alpha - beta = 180° - 78° 45'3" - 78° 45'3" = 22° 29'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 837.97 }{ 79.09 } = 10.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 66.18 }{ 2 * sin 78° 45'3" } = 33.74 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.18**2+2 * 25.82**2 - 66.18**2 } }{ 2 } = 37.793 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.82**2+2 * 66.18**2 - 66.18**2 } }{ 2 } = 37.793 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 66.18**2+2 * 66.18**2 - 25.82**2 } }{ 2 } = 64.909 ; ;
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