Triangle calculator - result

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: h_a = 2.69547808397
Height: h_b = 1.79765205598
Height: h_c = 1.34773904199

Median: m_a = 3.14660489677
Median: m_b = 2.58326610279
Median: m_c = 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

Calculate another triangle

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.

$a = 1.86 ; ; b = 2.78 ; ; c = 3.71 ; ;$

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

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

2. Semiperimeter of the triangle

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

3. The triangle area using Heron's formula

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

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

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

5. Calculation of the inner angles of the triangle using a Law of Cosines

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

6. Inradius

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

7. Circumradius

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

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