Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 0.5   b = 0.45   c = 0.5

Area: T = 0.11004657124
Perimeter: p = 1.45
Semiperimeter: s = 0.725

Angle ∠ A = α = 63.25663160496° = 63°15'23″ = 1.10440309877 rad
Angle ∠ B = β = 53.48773679008° = 53°29'15″ = 0.93435306781 rad
Angle ∠ C = γ = 63.25663160496° = 63°15'23″ = 1.10440309877 rad

Height: ha = 0.40218628497
Height: hb = 0.44765142775
Height: hc = 0.40218628497

Median: ma = 0.40546603514
Median: mb = 0.44765142775
Median: mc = 0.40546603514

Inradius: r = 0.13985733965
Circumradius: R = 0.28799462555

Vertex coordinates: A[0.5; 0] B[0; 0] C[0.29875; 0.40218628497]
Centroid: CG[0.26658333333; 0.13439542832]
Coordinates of the circumscribed circle: U[0.25; 0.1265975815]
Coordinates of the inscribed circle: I[0.275; 0.13985733965]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 116.744368395° = 116°44'37″ = 1.10440309877 rad
∠ B' = β' = 126.5132632099° = 126°30'45″ = 0.93435306781 rad
∠ C' = γ' = 116.744368395° = 116°44'37″ = 1.10440309877 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 = 0.5+0.45+0.5 = 1.45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1.45 }{ 2 } = 0.73 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.73 * (0.73-0.5)(0.73-0.45)(0.73-0.5) } ; ; T = sqrt{ 0.01 } = 0.1 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.1 }{ 0.5 } = 0.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.1 }{ 0.45 } = 0.45 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.1 }{ 0.5 } = 0.4 ; ;

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{ 0.45**2+0.5**2-0.5**2 }{ 2 * 0.45 * 0.5 } ) = 63° 15'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.5**2+0.5**2-0.45**2 }{ 2 * 0.5 * 0.5 } ) = 53° 29'15" ; ; gamma = 180° - alpha - beta = 180° - 63° 15'23" - 53° 29'15" = 63° 15'23" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.1 }{ 0.73 } = 0.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.5 }{ 2 * sin 63° 15'23" } = 0.28 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.45**2+2 * 0.5**2 - 0.5**2 } }{ 2 } = 0.405 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.5**2+2 * 0.5**2 - 0.45**2 } }{ 2 } = 0.447 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.45**2+2 * 0.5**2 - 0.5**2 } }{ 2 } = 0.405 ; ;
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