Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 5   b = 5   c = 7

Area: T = 12.497749975
Perimeter: p = 17
Semiperimeter: s = 8.5

Angle ∠ A = α = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ B = β = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ C = γ = 88.85440080016° = 88°51'14″ = 1.55107949932 rad

Height: ha = 4.99989999
Height: hb = 4.99989999
Height: hc = 3.57107142143

Median: ma = 5.54552682532
Median: mb = 5.54552682532
Median: mc = 3.57107142143

Inradius: r = 1.47702940882
Circumradius: R = 3.50107002101

Vertex coordinates: A[7; 0] B[0; 0] C[3.5; 3.57107142143]
Centroid: CG[3.5; 1.19902380714]
Coordinates of the circumscribed circle: U[3.5; 0.07700140042]
Coordinates of the inscribed circle: I[3.5; 1.47702940882]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ B' = β' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ C' = γ' = 91.14659919984° = 91°8'46″ = 1.55107949932 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 = 5+5+7 = 17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17 }{ 2 } = 8.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.5 * (8.5-5)(8.5-5)(8.5-7) } ; ; T = sqrt{ 156.19 } = 12.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 12.5 }{ 5 } = 5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 12.5 }{ 5 } = 5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 12.5 }{ 7 } = 3.57 ; ;

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{ 5**2+7**2-5**2 }{ 2 * 5 * 7 } ) = 45° 34'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+7**2-5**2 }{ 2 * 5 * 7 } ) = 45° 34'23" ; ; gamma = 180° - alpha - beta = 180° - 45° 34'23" - 45° 34'23" = 88° 51'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 12.5 }{ 8.5 } = 1.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 45° 34'23" } = 3.5 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5**2+2 * 7**2 - 5**2 } }{ 2 } = 5.545 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 5**2 - 5**2 } }{ 2 } = 5.545 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5**2+2 * 5**2 - 7**2 } }{ 2 } = 3.571 ; ;
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