Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 3.6   b = 7.9   c = 6.6

Area: T = 11.78883902103
Perimeter: p = 18.1
Semiperimeter: s = 9.05

Angle ∠ A = α = 26.88437786993° = 26°53'2″ = 0.46992104537 rad
Angle ∠ B = β = 97.12199972892° = 97°7'12″ = 1.69550637222 rad
Angle ∠ C = γ = 55.99662240115° = 55°59'46″ = 0.97773184777 rad

Height: ha = 6.54991056724
Height: hb = 2.98444025849
Height: hc = 3.57222394577

Median: ma = 7.05330135403
Median: mb = 3.55877380454
Median: mc = 5.17663887026

Inradius: r = 1.30325845536
Circumradius: R = 3.98106961903

Vertex coordinates: A[6.6; 0] B[0; 0] C[-0.44662121212; 3.57222394577]
Centroid: CG[2.05112626263; 1.19107464859]
Coordinates of the circumscribed circle: U[3.3; 2.22661945467]
Coordinates of the inscribed circle: I[1.15; 1.30325845536]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.1166221301° = 153°6'58″ = 0.46992104537 rad
∠ B' = β' = 82.88800027108° = 82°52'48″ = 1.69550637222 rad
∠ C' = γ' = 124.0043775989° = 124°14″ = 0.97773184777 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 3.6 ; ; b = 7.9 ; ; c = 6.6 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 3.6 ; ; b = 7.9 ; ; c = 6.6 ; ; : Nr. 1

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

p = a+b+c = 3.6+7.9+6.6 = 18.1 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.1 }{ 2 } = 9.05 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.05 * (9.05-3.6)(9.05-7.9)(9.05-6.6) } ; ; T = sqrt{ 138.97 } = 11.79 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.79 }{ 3.6 } = 6.55 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.79 }{ 7.9 } = 2.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.79 }{ 6.6 } = 3.57 ; ;

6. 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{ 3.6**2-7.9**2-6.6**2 }{ 2 * 7.9 * 6.6 } ) = 26° 53'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.9**2-3.6**2-6.6**2 }{ 2 * 3.6 * 6.6 } ) = 97° 7'12" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.6**2-3.6**2-7.9**2 }{ 2 * 7.9 * 3.6 } ) = 55° 59'46" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.79 }{ 9.05 } = 1.3 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.6 }{ 2 * sin 26° 53'2" } = 3.98 ; ;




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