Triangle calculator - result

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

You have entered area T and aspect ratio a:b:c = 2:3:4.

Obtuse scalene triangle.

Sides: a = 1.85554384558   b = 2.78331576837   c = 3.71108769116

Area: T = 2.5
Perimeter: p = 8.34994730511
Semiperimeter: s = 4.17547365256

Angle ∠ A = α = 28.95550243719° = 28°57'18″ = 0.50553605103 rad
Angle ∠ B = β = 46.56774634422° = 46°34'3″ = 0.81327555614 rad
Angle ∠ C = γ = 104.4787512186° = 104°28'39″ = 1.82334765819 rad

Height: ha = 2.69547808397
Height: hb = 1.79765205598
Height: hc = 1.34773904199

Median: ma = 3.14660489677
Median: mb = 2.58326610279
Median: mc = 1.46768528947

Inradius: r = 0.59988401866
Circumradius: R = 1.91662885971

Vertex coordinates: A[3.71108769116; 0] B[0; 0] C[1.27656139384; 1.34773904199]
Centroid: CG[1.66221636167; 0.449913014]
Coordinates of the circumscribed circle: U[1.85554384558; -0.47990721493]
Coordinates of the inscribed circle: I[1.39215788419; 0.59988401866]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 151.0454975628° = 151°2'42″ = 0.50553605103 rad
∠ B' = β' = 133.4332536558° = 133°25'57″ = 0.81327555614 rad
∠ C' = γ' = 75.52224878141° = 75°31'21″ = 1.82334765819 rad

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How did we calculate this triangle?

1. Input data entered: area T and aspect ratio a:b:c.

T = 2.5 ; ; a:b:c = 2:3:4 ; ;

2. From side a and angle β we calculate height hc:

h_c = a * sin beta = 1.855 * sin 46° 34'3" = 1.347 ; ;
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 = 1.86 ; ; b = 2.78 ; ; c = 3.71 ; ;

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

p = a+b+c = 1.86+2.78+3.71 = 8.35 ; ;

4. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 8.35 }{ 2 } = 4.17 ; ;

5. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.17 * (4.17-1.86)(4.17-2.78)(4.17-3.71) } ; ; T = sqrt{ 6.25 } = 2.5 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.5 }{ 1.86 } = 2.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.5 }{ 2.78 } = 1.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.5 }{ 3.71 } = 1.35 ; ;

7. 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 2.78**2+3.71**2-1.86**2 }{ 2 * 2.78 * 3.71 } ) = 28° 57'18" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.86**2+3.71**2-2.78**2 }{ 2 * 1.86 * 3.71 } ) = 46° 34'3" ; ;
gamma = 180° - alpha - beta = 180° - 28° 57'18" - 46° 34'3" = 104° 28'39" ; ;

8. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.5 }{ 4.17 } = 0.6 ; ;

9. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.86 }{ 2 * sin 28° 57'18" } = 1.92 ; ;

10. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.78**2+2 * 3.71**2 - 1.86**2 } }{ 2 } = 3.146 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.71**2+2 * 1.86**2 - 2.78**2 } }{ 2 } = 2.583 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.78**2+2 * 1.86**2 - 3.71**2 } }{ 2 } = 1.467 ; ;
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