Triangle calculator

You have entered side a, b and angle γ.

Right scalene triangle.

Sides: a = 490 b = 960 c = 1077.822187768

Area: T = 235200
Perimeter: p = 2527.822187768
Semiperimeter: s = 1263.911093884

Angle ∠ A = α = 27.04105239095° = 27°2'26″ = 0.47219461737 rad
Angle ∠ B = β = 62.95994760905° = 62°57'34″ = 1.09988501531 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: h_a = 960
Height: h_b = 490
Height: h_c = 436.4365750417

Median: m_a = 990.7769902652
Median: m_b = 685.9330025586
Median: m_c = 538.9110938839

Inradius: r = 186.0899061161
Circumradius: R = 538.9110938839

Vertex coordinates: A[1077.822187768; 0] B[0; 0] C[222.7644080942; 436.4365750417]
Centroid: CG[433.5298652873; 145.4798583472]
Coordinates of the circumscribed circle: U[538.9110938839; 0]
Coordinates of the inscribed circle: I[303.9110938839; 186.0899061161]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.959947609° = 152°57'34″ = 0.47219461737 rad
∠ B' = β' = 117.041052391° = 117°2'26″ = 1.09988501531 rad
∠ C' = γ' = 90° = 1.57107963268 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.

$a = 490 ; ; b = 960 ; ; c = 1077.82 ; ;$

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

$p = a+b+c = 490+960+1077.82 = 2527.82 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 2527.82 }{ 2 } = 1263.91 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1263.91 * (1263.91-490)(1263.91-960)(1263.91-1077.82) } ; ; T = sqrt{ 55319040000 } = 235200 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 235200 }{ 490 } = 960 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 235200 }{ 960 } = 490 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 235200 }{ 1077.82 } = 436.44 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 490**2-960**2-1077.82**2 }{ 2 * 960 * 1077.82 } ) = 27° 2'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 960**2-490**2-1077.82**2 }{ 2 * 490 * 1077.82 } ) = 62° 57'34" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 1077.82**2-490**2-960**2 }{ 2 * 960 * 490 } ) = 90° ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 235200 }{ 1263.91 } = 186.09 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 490 }{ 2 * sin 27° 2'26" } = 538.91 ; ;$

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