Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 10   b = 29   c = 29

Area: T = 142.8298568571
Perimeter: p = 68
Semiperimeter: s = 34

Angle ∠ A = α = 19.85663836846° = 19°51'23″ = 0.34765592728 rad
Angle ∠ B = β = 80.07218081577° = 80°4'19″ = 1.39875166904 rad
Angle ∠ C = γ = 80.07218081577° = 80°4'19″ = 1.39875166904 rad

Height: ha = 28.56657137142
Height: hb = 9.85502461083
Height: hc = 9.85502461083

Median: ma = 28.56657137142
Median: mb = 16.13222658049
Median: mc = 16.13222658049

Inradius: r = 4.20108402521
Circumradius: R = 14.72204443833

Vertex coordinates: A[29; 0] B[0; 0] C[1.7244137931; 9.85502461083]
Centroid: CG[10.24113793103; 3.28334153694]
Coordinates of the circumscribed circle: U[14.5; 2.53880076523]
Coordinates of the inscribed circle: I[5; 4.20108402521]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.1443616315° = 160°8'37″ = 0.34765592728 rad
∠ B' = β' = 99.92881918423° = 99°55'41″ = 1.39875166904 rad
∠ C' = γ' = 99.92881918423° = 99°55'41″ = 1.39875166904 rad

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How did we calculate this triangle?

a = 10 ; ; b = 29 ; ; c = 29 ; ;

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

p = a+b+c = 10+29+29 = 68 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68 }{ 2 } = 34 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34 * (34-10)(34-29)(34-29) } ; ; T = sqrt{ 20400 } = 142.83 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 142.83 }{ 10 } = 28.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 142.83 }{ 29 } = 9.85 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 142.83 }{ 29 } = 9.85 ; ;

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**2-10**2 }{ 2 * 29 * 29 } ) = 19° 51'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10**2+29**2-29**2 }{ 2 * 10 * 29 } ) = 80° 4'19" ; ; gamma = 180° - alpha - beta = 180° - 19° 51'23" - 80° 4'19" = 80° 4'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 142.83 }{ 34 } = 4.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10 }{ 2 * sin 19° 51'23" } = 14.72 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 29**2 - 10**2 } }{ 2 } = 28.566 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 10**2 - 29**2 } }{ 2 } = 16.132 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 29**2+2 * 10**2 - 29**2 } }{ 2 } = 16.132 ; ;
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