Triangle calculator

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

You have entered side b, c and angle α.

Obtuse scalene triangle.

Sides: a = 89.75106106817   b = 90   c = 0.25

Area: T = 0.78547603296
Perimeter: p = 180.0010610682
Semiperimeter: s = 900.0003053409

Angle ∠ A = α = 4° = 4° = 0.07698131701 rad
Angle ∠ B = β = 175.9898867063° = 175°59'20″ = 3.07215851771 rad
Angle ∠ C = γ = 0.0111132937° = 0°40″ = 00.0001943064 rad

Height: ha = 0.01774875764
Height: hb = 0.01774391184
Height: hc = 6.2788082637

Median: ma = 45.12546963487
Median: mb = 44.75106123854
Median: mc = 89.87553049167

Inradius: r = 0.00987195296
Circumradius: R = 643.3143845039

Vertex coordinates: A[0.25; 0] B[0; 0] C[-89.53107645234; 6.2788082637]
Centroid: CG[-29.76602548411; 2.09326942123]
Coordinates of the circumscribed circle: U[0.125; 643.3143832895]
Coordinates of the inscribed circle: I[00.0003053409; 0.00987195296]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 176° = 0.07698131701 rad
∠ B' = β' = 4.0111132937° = 4°40″ = 3.07215851771 rad
∠ C' = γ' = 179.9898867063° = 179°59'20″ = 00.0001943064 rad

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How did we calculate this triangle?

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 = 89.75 ; ; b = 90 ; ; c = 0.25 ; ;

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

p = a+b+c = 89.75+90+0.25 = 180 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-89.75)(90-90)(90-0.25) } ; ; T = sqrt{ 0.62 } = 0.78 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.78 }{ 89.75 } = 0.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.78 }{ 90 } = 0.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.78 }{ 0.25 } = 6.28 ; ;

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{ 89.75**2-90**2-0.25**2 }{ 2 * 90 * 0.25 } ) = 4° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 90**2-89.75**2-0.25**2 }{ 2 * 89.75 * 0.25 } ) = 175° 59'20" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.25**2-89.75**2-90**2 }{ 2 * 90 * 89.75 } ) = 0° 40" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.78 }{ 90 } = 0.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 89.75 }{ 2 * sin 4° } = 643.31 ; ;




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