Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 7   b = 11   c = 11

Area: T = 36.49991438256
Perimeter: p = 29
Semiperimeter: s = 14.5

Angle ∠ A = α = 37.106600907° = 37°6'22″ = 0.64876220305 rad
Angle ∠ B = β = 71.4476995465° = 71°26'49″ = 1.24769853115 rad
Angle ∠ C = γ = 71.4476995465° = 71°26'49″ = 1.24769853115 rad

Height: ha = 10.42883268073
Height: hb = 6.63662079683
Height: hc = 6.63662079683

Median: ma = 10.42883268073
Median: mb = 7.39993242935
Median: mc = 7.39993242935

Inradius: r = 2.51771823328
Circumradius: R = 5.8021505948

Vertex coordinates: A[11; 0] B[0; 0] C[2.22772727273; 6.63662079683]
Centroid: CG[4.40990909091; 2.21220693228]
Coordinates of the circumscribed circle: U[5.5; 1.84659337107]
Coordinates of the inscribed circle: I[3.5; 2.51771823328]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.894399093° = 142°53'38″ = 0.64876220305 rad
∠ B' = β' = 108.5533004535° = 108°33'11″ = 1.24769853115 rad
∠ C' = γ' = 108.5533004535° = 108°33'11″ = 1.24769853115 rad

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How did we calculate this triangle?

a = 7 ; ; b = 11 ; ; c = 11 ; ;

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

p = a+b+c = 7+11+11 = 29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29 }{ 2 } = 14.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.5 * (14.5-7)(14.5-11)(14.5-11) } ; ; T = sqrt{ 1332.19 } = 36.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.5 }{ 7 } = 10.43 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.5 }{ 11 } = 6.64 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.5 }{ 11 } = 6.64 ; ;

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{ 11**2+11**2-7**2 }{ 2 * 11 * 11 } ) = 37° 6'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+11**2-11**2 }{ 2 * 7 * 11 } ) = 71° 26'49" ; ; gamma = 180° - alpha - beta = 180° - 37° 6'22" - 71° 26'49" = 71° 26'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.5 }{ 14.5 } = 2.52 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 37° 6'22" } = 5.8 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 11**2 - 7**2 } }{ 2 } = 10.428 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 7**2 - 11**2 } }{ 2 } = 7.399 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 11**2+2 * 7**2 - 11**2 } }{ 2 } = 7.399 ; ;
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