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 = 3.2   b = 7.6   c = 6.4

Area: T = 10.10878187558
Perimeter: p = 17.2
Semiperimeter: s = 8.6

Angle ∠ A = α = 24.55882124119° = 24°33'30″ = 0.4298621665 rad
Angle ∠ B = β = 99.2165965643° = 99°12'57″ = 1.7321645271 rad
Angle ∠ C = γ = 56.22658219451° = 56°13'33″ = 0.98113257176 rad

Height: ha = 6.31773867224
Height: hb = 2.66599523042
Height: hc = 3.15986933612

Median: ma = 6.84110525506
Median: mb = 3.34106586177
Median: mc = 4.87444230428

Inradius: r = 1.17553277623
Circumradius: R = 3.85496930881

Vertex coordinates: A[6.4; 0] B[0; 0] C[-0.51225; 3.15986933612]
Centroid: CG[1.96325; 1.05328977871]
Coordinates of the circumscribed circle: U[3.2; 2.14401254338]
Coordinates of the inscribed circle: I[1; 1.17553277623]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.4421787588° = 155°26'30″ = 0.4298621665 rad
∠ B' = β' = 80.7844034357° = 80°47'3″ = 1.7321645271 rad
∠ C' = γ' = 123.7744178055° = 123°46'27″ = 0.98113257176 rad

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How did we calculate this triangle?

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

a = 3.2 ; ; b = 7.6 ; ; c = 6.4 ; ;


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 = 3.2 ; ; b = 7.6 ; ; c = 6.4 ; ; : Nr. 1

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

p = a+b+c = 3.2+7.6+6.4 = 17.2 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.2 }{ 2 } = 8.6 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.6 * (8.6-3.2)(8.6-7.6)(8.6-6.4) } ; ; T = sqrt{ 102.17 } = 10.11 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.11 }{ 3.2 } = 6.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.11 }{ 7.6 } = 2.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.11 }{ 6.4 } = 3.16 ; ;

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{ 3.2**2-7.6**2-6.4**2 }{ 2 * 7.6 * 6.4 } ) = 24° 33'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 7.6**2-3.2**2-6.4**2 }{ 2 * 3.2 * 6.4 } ) = 99° 12'57" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 6.4**2-3.2**2-7.6**2 }{ 2 * 7.6 * 3.2 } ) = 56° 13'33" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.11 }{ 8.6 } = 1.18 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 3.2 }{ 2 * sin 24° 33'30" } = 3.85 ; ;




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