Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 27.25   b = 92   c = 95.95

Area: T = 1253.549999936
Perimeter: p = 215.2
Semiperimeter: s = 107.6

Angle ∠ A = α = 16.49992076038° = 16°29'57″ = 0.28879654967 rad
Angle ∠ B = β = 73.50326207418° = 73°30'9″ = 1.28328627408 rad
Angle ∠ C = γ = 89.99881716544° = 89°59'53″ = 1.57107644161 rad

Height: ha = 921.9999999532
Height: hb = 27.25499999861
Height: hc = 26.12881917532

Median: ma = 93.00330140641
Median: mb = 53.46547781254
Median: mc = 47.97658337603

Inradius: r = 11.65496282469
Circumradius: R = 47.97550000244

Vertex coordinates: A[95.95; 0] B[0; 0] C[7.73882230328; 26.12881917532]
Centroid: CG[34.56327410109; 8.70993972511]
Coordinates of the circumscribed circle: U[47.975; 0.00215309134]
Coordinates of the inscribed circle: I[15.6; 11.65496282469]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.5010792396° = 163°30'3″ = 0.28879654967 rad
∠ B' = β' = 106.4977379258° = 106°29'51″ = 1.28328627408 rad
∠ C' = γ' = 90.00218283456° = 90°7″ = 1.57107644161 rad

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How did we calculate this triangle?

a = 27.25 ; ; b = 92 ; ; c = 95.95 ; ;

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

p = a+b+c = 27.25+92+95.95 = 215.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 215.2 }{ 2 } = 107.6 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 107.6 * (107.6-27.25)(107.6-92)(107.6-95.95) } ; ; T = sqrt{ 1571262.25 } = 1253.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1253.5 }{ 27.25 } = 92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1253.5 }{ 92 } = 27.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1253.5 }{ 95.95 } = 26.13 ; ;

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{ 92**2+95.95**2-27.25**2 }{ 2 * 92 * 95.95 } ) = 16° 29'57" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 27.25**2+95.95**2-92**2 }{ 2 * 27.25 * 95.95 } ) = 73° 30'9" ; ; gamma = 180° - alpha - beta = 180° - 16° 29'57" - 73° 30'9" = 89° 59'53" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1253.5 }{ 107.6 } = 11.65 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 27.25 }{ 2 * sin 16° 29'57" } = 47.98 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 92**2+2 * 95.95**2 - 27.25**2 } }{ 2 } = 93.003 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 95.95**2+2 * 27.25**2 - 92**2 } }{ 2 } = 53.465 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 92**2+2 * 27.25**2 - 95.95**2 } }{ 2 } = 47.976 ; ;
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