Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse isosceles triangle.

Sides: a = 110   b = 77.78   c = 77.78

Area: T = 3024.864419695
Perimeter: p = 265.56
Semiperimeter: s = 132.78

Angle ∠ A = α = 90.00325722698° = 90°9″ = 1.57108412214 rad
Angle ∠ B = β = 44.99987138651° = 44°59'55″ = 0.78553757161 rad
Angle ∠ C = γ = 44.99987138651° = 44°59'55″ = 0.78553757161 rad

Height: ha = 54.99875308537
Height: hb = 77.78799999216
Height: hc = 77.78799999216

Median: ma = 54.99875308537
Median: mb = 86.96222452562
Median: mc = 86.96222452562

Inradius: r = 22.78110227214
Circumradius: R = 555.0000000554

Vertex coordinates: A[77.78; 0] B[0; 0] C[77.78334919002; 77.78799999216]
Centroid: CG[51.85444973001; 25.92766666405]
Coordinates of the circumscribed circle: U[38.89; 38.89217459893]
Coordinates of the inscribed circle: I[55; 22.78110227214]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 89.99774277302° = 89°59'51″ = 1.57108412214 rad
∠ B' = β' = 135.0011286135° = 135°5″ = 0.78553757161 rad
∠ C' = γ' = 135.0011286135° = 135°5″ = 0.78553757161 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 = 110+77.78+77.78 = 265.56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 265.56 }{ 2 } = 132.78 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 132.78 * (132.78-110)(132.78-77.78)(132.78-77.78) } ; ; T = sqrt{ 9149803.41 } = 3024.86 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3024.86 }{ 110 } = 55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3024.86 }{ 77.78 } = 77.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3024.86 }{ 77.78 } = 77.78 ; ;

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{ 77.78**2+77.78**2-110**2 }{ 2 * 77.78 * 77.78 } ) = 90° 9" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 110**2+77.78**2-77.78**2 }{ 2 * 110 * 77.78 } ) = 44° 59'55" ; ;
 gamma = 180° - alpha - beta = 180° - 90° 9" - 44° 59'55" = 44° 59'55" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3024.86 }{ 132.78 } = 22.78 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 110 }{ 2 * sin 90° 9" } = 55 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 77.78**2+2 * 77.78**2 - 110**2 } }{ 2 } = 54.998 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 77.78**2+2 * 110**2 - 77.78**2 } }{ 2 } = 86.962 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 77.78**2+2 * 110**2 - 77.78**2 } }{ 2 } = 86.962 ; ;
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