Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 25   b = 29   c = 29

Area: T = 327.0976602703
Perimeter: p = 83
Semiperimeter: s = 41.5

Angle ∠ A = α = 51.06664578882° = 51°3'59″ = 0.89112778275 rad
Angle ∠ B = β = 64.46767710559° = 64°28' = 1.12551574131 rad
Angle ∠ C = γ = 64.46767710559° = 64°28' = 1.12551574131 rad

Height: ha = 26.16877282163
Height: hb = 22.55883863933
Height: hc = 22.55883863933

Median: ma = 26.16877282163
Median: mb = 22.86437267303
Median: mc = 22.86437267303

Inradius: r = 7.88218458483
Circumradius: R = 16.06994117779

Vertex coordinates: A[29; 0] B[0; 0] C[10.7765862069; 22.55883863933]
Centroid: CG[13.25986206897; 7.51994621311]
Coordinates of the circumscribed circle: U[14.5; 6.92664705939]
Coordinates of the inscribed circle: I[12.5; 7.88218458483]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 128.9343542112° = 128°56'1″ = 0.89112778275 rad
∠ B' = β' = 115.5333228944° = 115°32' = 1.12551574131 rad
∠ C' = γ' = 115.5333228944° = 115°32' = 1.12551574131 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 = 25+29+29 = 83 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 83 }{ 2 } = 41.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41.5 * (41.5-25)(41.5-29)(41.5-29) } ; ; T = sqrt{ 106992.19 } = 327.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 327.1 }{ 25 } = 26.17 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 327.1 }{ 29 } = 22.56 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 327.1 }{ 29 } = 22.56 ; ;

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{ 29**2+29**2-25**2 }{ 2 * 29 * 29 } ) = 51° 3'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 25**2+29**2-29**2 }{ 2 * 25 * 29 } ) = 64° 28' ; ; gamma = 180° - alpha - beta = 180° - 51° 3'59" - 64° 28' = 64° 28' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 327.1 }{ 41.5 } = 7.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 25 }{ 2 * sin 51° 3'59" } = 16.07 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 29**2 - 25**2 } }{ 2 } = 26.168 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 25**2 - 29**2 } }{ 2 } = 22.864 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 25**2 - 29**2 } }{ 2 } = 22.864 ; ;
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