Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 10   b = 23   c = 23

Area: T = 112.2549721603
Perimeter: p = 56
Semiperimeter: s = 28

Angle ∠ A = α = 25.11217155972° = 25°6'42″ = 0.4388282118 rad
Angle ∠ B = β = 77.44441422014° = 77°26'39″ = 1.35216552678 rad
Angle ∠ C = γ = 77.44441422014° = 77°26'39″ = 1.35216552678 rad

Height: ha = 22.45499443206
Height: hb = 9.76108453568
Height: hc = 9.76108453568

Median: ma = 22.45499443206
Median: mb = 13.5
Median: mc = 13.5

Inradius: r = 4.00989186287
Circumradius: R = 11.78217664143

Vertex coordinates: A[23; 0] B[0; 0] C[2.17439130435; 9.76108453568]
Centroid: CG[8.39113043478; 3.25436151189]
Coordinates of the circumscribed circle: U[11.5; 2.56112535683]
Coordinates of the inscribed circle: I[5; 4.00989186287]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 154.8888284403° = 154°53'18″ = 0.4388282118 rad
∠ B' = β' = 102.5565857799° = 102°33'21″ = 1.35216552678 rad
∠ C' = γ' = 102.5565857799° = 102°33'21″ = 1.35216552678 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 = 10+23+23 = 56 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 56 }{ 2 } = 28 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28 * (28-10)(28-23)(28-23) } ; ; T = sqrt{ 12600 } = 112.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 112.25 }{ 10 } = 22.45 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 112.25 }{ 23 } = 9.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 112.25 }{ 23 } = 9.76 ; ;

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{ 23**2+23**2-10**2 }{ 2 * 23 * 23 } ) = 25° 6'42" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+23**2-23**2 }{ 2 * 10 * 23 } ) = 77° 26'39" ; ; gamma = 180° - alpha - beta = 180° - 25° 6'42" - 77° 26'39" = 77° 26'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 112.25 }{ 28 } = 4.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 25° 6'42" } = 11.78 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 23**2 - 10**2 } }{ 2 } = 22.45 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 10**2 - 23**2 } }{ 2 } = 13.5 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 10**2 - 23**2 } }{ 2 } = 13.5 ; ;
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