Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 6.51   b = 1.1   c = 6.6

Area: T = 3.58804920925
Perimeter: p = 14.21
Semiperimeter: s = 7.105

Angle ∠ A = α = 80.52663696004° = 80°31'35″ = 1.40554502842 rad
Angle ∠ B = β = 9.59440468381° = 9°35'39″ = 0.16774477059 rad
Angle ∠ C = γ = 89.88795835614° = 89°52'46″ = 1.56986946635 rad

Height: ha = 1.10999975707
Height: hb = 6.51099856227
Height: hc = 1.08549976038

Median: ma = 3.43436533022
Median: mb = 6.53220402632
Median: mc = 3.30222795157

Inradius: r = 0.50439397737
Circumradius: R = 3.3300007288

Vertex coordinates: A[6.6; 0] B[0; 0] C[6.41989469697; 1.08549976038]
Centroid: CG[4.34396489899; 0.36216658679]
Coordinates of the circumscribed circle: U[3.3; 0.00769354992]
Coordinates of the inscribed circle: I[6.005; 0.50439397737]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 99.47436303996° = 99°28'25″ = 1.40554502842 rad
∠ B' = β' = 170.4065953162° = 170°24'21″ = 0.16774477059 rad
∠ C' = γ' = 90.12204164386° = 90°7'14″ = 1.56986946635 rad

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How did we calculate this triangle?

a = 6.51 ; ; b = 1.1 ; ; c = 6.6 ; ;

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

p = a+b+c = 6.51+1.1+6.6 = 14.21 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14.21 }{ 2 } = 7.11 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.11 * (7.11-6.51)(7.11-1.1)(7.11-6.6) } ; ; T = sqrt{ 12.82 } = 3.58 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3.58 }{ 6.51 } = 1.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3.58 }{ 1.1 } = 6.51 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3.58 }{ 6.6 } = 1.08 ; ;

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{ 6.51**2-1.1**2-6.6**2 }{ 2 * 1.1 * 6.6 } ) = 80° 31'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 1.1**2-6.51**2-6.6**2 }{ 2 * 6.51 * 6.6 } ) = 9° 35'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.6**2-6.51**2-1.1**2 }{ 2 * 1.1 * 6.51 } ) = 89° 52'46" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3.58 }{ 7.11 } = 0.5 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 6.51 }{ 2 * sin 80° 31'35" } = 3.3 ; ;

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