Triangle calculator

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

You have entered side a, b and c.

Acute isosceles triangle.

Sides: a = 180   b = 180   c = 4.25

Area: T = 382.473334434
Perimeter: p = 364.25
Semiperimeter: s = 182.125

Angle ∠ A = α = 89.32435757789° = 89°19'25″ = 1.5598990497 rad
Angle ∠ B = β = 89.32435757789° = 89°19'25″ = 1.5598990497 rad
Angle ∠ C = γ = 1.35328484422° = 1°21'10″ = 0.02436116596 rad

Height: ha = 4.2549703826
Height: hb = 4.2549703826
Height: hc = 179.987745616

Median: ma = 90.05501596334
Median: mb = 90.05501596334
Median: mc = 179.987745616

Inradius: r = 2.11000595434
Circumradius: R = 90.0066272357

Vertex coordinates: A[4.25; 0] B[0; 0] C[2.125; 179.987745616]
Centroid: CG[2.125; 59.996581872]
Coordinates of the circumscribed circle: U[2.125; 89.98111838031]
Coordinates of the inscribed circle: I[2.125; 2.11000595434]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.67664242211° = 90°40'35″ = 1.5598990497 rad
∠ B' = β' = 90.67664242211° = 90°40'35″ = 1.5598990497 rad
∠ C' = γ' = 178.6477151558° = 178°38'50″ = 0.02436116596 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 = 180 ; ; b = 180 ; ; c = 4.25 ; ;

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

p = a+b+c = 180+180+4.25 = 364.25 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 364.25 }{ 2 } = 182.13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 182.13 * (182.13-180)(182.13-180)(182.13-4.25) } ; ; T = sqrt{ 146285.86 } = 382.47 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 382.47 }{ 180 } = 4.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 382.47 }{ 180 } = 4.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 382.47 }{ 4.25 } = 179.99 ; ;

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{ 180**2-180**2-4.25**2 }{ 2 * 180 * 4.25 } ) = 89° 19'25" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 180**2-180**2-4.25**2 }{ 2 * 180 * 4.25 } ) = 89° 19'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.25**2-180**2-180**2 }{ 2 * 180 * 180 } ) = 1° 21'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 382.47 }{ 182.13 } = 2.1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 180 }{ 2 * sin 89° 19'25" } = 90.01 ; ;




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