Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 1.81   b = 7.47   c = 7.25

Area: T = 6.56112432307
Perimeter: p = 16.53
Semiperimeter: s = 8.265

Angle ∠ A = α = 14.02224635239° = 14°1'21″ = 0.24547381577 rad
Angle ∠ B = β = 89.9187696642° = 89°55'4″ = 1.56993598622 rad
Angle ∠ C = γ = 76.06598398341° = 76°3'35″ = 1.32774946336 rad

Height: ha = 7.25499925201
Height: hb = 1.7576691628
Height: hc = 1.81099981326

Median: ma = 7.30549760438
Median: mb = 3.73875225752
Median: mc = 4.04994289721

Inradius: r = 0.79438588301
Circumradius: R = 3.73550038535

Vertex coordinates: A[7.25; 0] B[0; 0] C[0.00326; 1.81099981326]
Centroid: CG[2.41875333333; 0.60333327109]
Coordinates of the circumscribed circle: U[3.625; 0.9899793746]
Coordinates of the inscribed circle: I[0.795; 0.79438588301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.9787536476° = 165°58'39″ = 0.24547381577 rad
∠ B' = β' = 90.0822303358° = 90°4'56″ = 1.56993598622 rad
∠ C' = γ' = 103.9440160166° = 103°56'25″ = 1.32774946336 rad

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How did we calculate this triangle?

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

p = a+b+c = 1.81+7.47+7.25 = 16.53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.53 }{ 2 } = 8.27 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.27 * (8.27-1.81)(8.27-7.47)(8.27-7.25) } ; ; T = sqrt{ 43.05 } = 6.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 6.56 }{ 1.81 } = 7.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 6.56 }{ 7.47 } = 1.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 6.56 }{ 7.25 } = 1.81 ; ;

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{ 7.47**2+7.25**2-1.81**2 }{ 2 * 7.47 * 7.25 } ) = 14° 1'21" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.81**2+7.25**2-7.47**2 }{ 2 * 1.81 * 7.25 } ) = 89° 55'4" ; ; gamma = 180° - alpha - beta = 180° - 14° 1'21" - 89° 55'4" = 76° 3'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 6.56 }{ 8.27 } = 0.79 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.81 }{ 2 * sin 14° 1'21" } = 3.74 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.47**2+2 * 7.25**2 - 1.81**2 } }{ 2 } = 7.305 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.25**2+2 * 1.81**2 - 7.47**2 } }{ 2 } = 3.738 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.47**2+2 * 1.81**2 - 7.25**2 } }{ 2 } = 4.049 ; ;
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