Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 109.91   b = 102   c = 102

Area: T = 4722.278773796
Perimeter: p = 313.91
Semiperimeter: s = 156.955

Angle ∠ A = α = 65.20105066528° = 65°12'2″ = 1.13879635151 rad
Angle ∠ B = β = 57.43997466736° = 57°23'59″ = 1.00218145693 rad
Angle ∠ C = γ = 57.43997466736° = 57°23'59″ = 1.00218145693 rad

Height: ha = 85.93299015186
Height: hb = 92.59436811364
Height: hc = 92.59436811364

Median: ma = 85.93299015186
Median: mb = 92.95875389627
Median: mc = 92.95875389627

Inradius: r = 30.08768257651
Circumradius: R = 60.53877163021

Vertex coordinates: A[102; 0] B[0; 0] C[59.21767063725; 92.59436811364]
Centroid: CG[53.73989021242; 30.86545603788]
Coordinates of the circumscribed circle: U[51; 32.61661784253]
Coordinates of the inscribed circle: I[54.955; 30.08768257651]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 114.7999493347° = 114°47'58″ = 1.13879635151 rad
∠ B' = β' = 122.6600253326° = 122°36'1″ = 1.00218145693 rad
∠ C' = γ' = 122.6600253326° = 122°36'1″ = 1.00218145693 rad

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How did we calculate this triangle?

a = 109.91 ; ; b = 102 ; ; c = 102 ; ;

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

p = a+b+c = 109.91+102+102 = 313.91 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 313.91 }{ 2 } = 156.96 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 156.96 * (156.96-109.91)(156.96-102)(156.96-102) } ; ; T = sqrt{ 22299907.03 } = 4722.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4722.28 }{ 109.91 } = 85.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4722.28 }{ 102 } = 92.59 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4722.28 }{ 102 } = 92.59 ; ;

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{ 102**2+102**2-109.91**2 }{ 2 * 102 * 102 } ) = 65° 12'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 109.91**2+102**2-102**2 }{ 2 * 109.91 * 102 } ) = 57° 23'59" ; ; gamma = 180° - alpha - beta = 180° - 65° 12'2" - 57° 23'59" = 57° 23'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4722.28 }{ 156.96 } = 30.09 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 109.91 }{ 2 * sin 65° 12'2" } = 60.54 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 102**2+2 * 102**2 - 109.91**2 } }{ 2 } = 85.93 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 102**2+2 * 109.91**2 - 102**2 } }{ 2 } = 92.958 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 102**2+2 * 109.91**2 - 102**2 } }{ 2 } = 92.958 ; ;
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