Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 5   b = 8   c = 8

Area: T = 18.9988355192
Perimeter: p = 21
Semiperimeter: s = 10.5

Angle ∠ A = α = 36.42199137286° = 36°25'12″ = 0.63656474079 rad
Angle ∠ B = β = 71.79900431357° = 71°47'24″ = 1.25329726229 rad
Angle ∠ C = γ = 71.79900431357° = 71°47'24″ = 1.25329726229 rad

Height: ha = 7.59993420768
Height: hb = 4.7549588798
Height: hc = 4.7549588798

Median: ma = 7.59993420768
Median: mb = 5.3398539126
Median: mc = 5.3398539126

Inradius: r = 1.80993671611
Circumradius: R = 4.21108908477

Vertex coordinates: A[8; 0] B[0; 0] C[1.56325; 4.7549588798]
Centroid: CG[3.18875; 1.5833196266]
Coordinates of the circumscribed circle: U[4; 1.31659033899]
Coordinates of the inscribed circle: I[2.5; 1.80993671611]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.5880086271° = 143°34'48″ = 0.63656474079 rad
∠ B' = β' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad
∠ C' = γ' = 108.2109956864° = 108°12'36″ = 1.25329726229 rad

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How did we calculate this triangle?

a = 5 ; ; b = 8 ; ; c = 8 ; ;

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

p = a+b+c = 5+8+8 = 21 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21 }{ 2 } = 10.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.5 * (10.5-5)(10.5-8)(10.5-8) } ; ; T = sqrt{ 360.94 } = 19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 19 }{ 5 } = 7.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 19 }{ 8 } = 4.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 19 }{ 8 } = 4.75 ; ;

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{ 8**2+8**2-5**2 }{ 2 * 8 * 8 } ) = 36° 25'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 5**2+8**2-8**2 }{ 2 * 5 * 8 } ) = 71° 47'24" ; ; gamma = 180° - alpha - beta = 180° - 36° 25'12" - 71° 47'24" = 71° 47'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 19 }{ 10.5 } = 1.81 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 5 }{ 2 * sin 36° 25'12" } = 4.21 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 8**2 - 5**2 } }{ 2 } = 7.599 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 5**2 - 8**2 } }{ 2 } = 5.339 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 5**2 - 8**2 } }{ 2 } = 5.339 ; ;
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