Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 22   b = 27   c = 27

Area: T = 271.2344216131
Perimeter: p = 76
Semiperimeter: s = 38

Angle ∠ A = α = 48.08441518115° = 48°5'3″ = 0.83992267671 rad
Angle ∠ B = β = 65.95879240942° = 65°57'29″ = 1.15111829432 rad
Angle ∠ C = γ = 65.95879240942° = 65°57'29″ = 1.15111829432 rad

Height: ha = 24.65876560119
Height: hb = 20.09114234171
Height: hc = 20.09114234171

Median: ma = 24.65876560119
Median: mb = 20.5977329924
Median: mc = 20.5977329924

Inradius: r = 7.13877425298
Circumradius: R = 14.78224270005

Vertex coordinates: A[27; 0] B[0; 0] C[8.9632962963; 20.09114234171]
Centroid: CG[11.9887654321; 6.6977141139]
Coordinates of the circumscribed circle: U[13.5; 6.02224702595]
Coordinates of the inscribed circle: I[11; 7.13877425298]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.9165848188° = 131°54'57″ = 0.83992267671 rad
∠ B' = β' = 114.0422075906° = 114°2'31″ = 1.15111829432 rad
∠ C' = γ' = 114.0422075906° = 114°2'31″ = 1.15111829432 rad

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How did we calculate this triangle?

a = 22 ; ; b = 27 ; ; c = 27 ; ;

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

p = a+b+c = 22+27+27 = 76 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 76 }{ 2 } = 38 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 38 * (38-22)(38-27)(38-27) } ; ; T = sqrt{ 73568 } = 271.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 271.23 }{ 22 } = 24.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 271.23 }{ 27 } = 20.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 271.23 }{ 27 } = 20.09 ; ;

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{ 22**2-27**2-27**2 }{ 2 * 27 * 27 } ) = 48° 5'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 27**2-22**2-27**2 }{ 2 * 22 * 27 } ) = 65° 57'29" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-22**2-27**2 }{ 2 * 27 * 22 } ) = 65° 57'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 271.23 }{ 38 } = 7.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 48° 5'3" } = 14.78 ; ;

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