Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 166.16   b = 166.16   c = 200

Area: T = 13269.94655914
Perimeter: p = 532.32
Semiperimeter: s = 266.16

Angle ∠ A = α = 52.9998956955° = 52°59'56″ = 0.9255006299 rad
Angle ∠ B = β = 52.9998956955° = 52°59'56″ = 0.9255006299 rad
Angle ∠ C = γ = 74.002208609° = 74°8″ = 1.29215800556 rad

Height: ha = 159.7254910826
Height: hb = 159.7254910826
Height: hc = 132.6999455914

Median: ma = 164.0199164734
Median: mb = 164.0199164734
Median: mc = 132.6999455914

Inradius: r = 49.85770243141
Circumradius: R = 104.0298857578

Vertex coordinates: A[200; 0] B[0; 0] C[100; 132.6999455914]
Centroid: CG[100; 44.23331519715]
Coordinates of the circumscribed circle: U[100; 28.67105983365]
Coordinates of the inscribed circle: I[100; 49.85770243141]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 127.0011043045° = 127°4″ = 0.9255006299 rad
∠ B' = β' = 127.0011043045° = 127°4″ = 0.9255006299 rad
∠ C' = γ' = 105.998791391° = 105°59'52″ = 1.29215800556 rad

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How did we calculate this triangle?

a = 166.16 ; ; b = 166.16 ; ; c = 200 ; ;

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

p = a+b+c = 166.16+166.16+200 = 532.32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 532.32 }{ 2 } = 266.16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 266.16 * (266.16-166.16)(266.16-166.16)(266.16-200) } ; ; T = sqrt{ 176091456 } = 13269.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13269.95 }{ 166.16 } = 159.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13269.95 }{ 166.16 } = 159.72 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13269.95 }{ 200 } = 132.7 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 166.16**2-166.16**2-200**2 }{ 2 * 166.16 * 200 } ) = 52° 59'56" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 166.16**2-166.16**2-200**2 }{ 2 * 166.16 * 200 } ) = 52° 59'56" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 200**2-166.16**2-166.16**2 }{ 2 * 166.16 * 166.16 } ) = 74° 8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13269.95 }{ 266.16 } = 49.86 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 166.16 }{ 2 * sin 52° 59'56" } = 104.03 ; ;

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