4 17 20 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 17   c = 20

Area: T = 24.33297657202
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 8.22882116737° = 8°13'42″ = 0.14436093853 rad
Angle ∠ B = β = 37.46326510725° = 37°27'46″ = 0.65438466077 rad
Angle ∠ C = γ = 134.3099137254° = 134°18'33″ = 2.34441366606 rad

Height: ha = 12.16548828601
Height: hb = 2.86223253788
Height: hc = 2.4332976572

Median: ma = 18.45326420872
Median: mb = 11.65111801977
Median: mc = 7.24656883731

Inradius: r = 1.187681784
Circumradius: R = 13.97546516226

Vertex coordinates: A[20; 0] B[0; 0] C[3.175; 2.4332976572]
Centroid: CG[7.725; 0.81109921907]
Coordinates of the circumscribed circle: U[10; -9.76217051776]
Coordinates of the inscribed circle: I[3.5; 1.187681784]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 171.7721788326° = 171°46'18″ = 0.14436093853 rad
∠ B' = β' = 142.5377348927° = 142°32'14″ = 0.65438466077 rad
∠ C' = γ' = 45.69108627462° = 45°41'27″ = 2.34441366606 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 = 4 ; ; b = 17 ; ; c = 20 ; ;

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

p = a+b+c = 4+17+20 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-4)(20.5-17)(20.5-20) } ; ; T = sqrt{ 591.94 } = 24.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24.33 }{ 4 } = 12.16 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24.33 }{ 17 } = 2.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24.33 }{ 20 } = 2.43 ; ;

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{ 4**2-17**2-20**2 }{ 2 * 17 * 20 } ) = 8° 13'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-4**2-20**2 }{ 2 * 4 * 20 } ) = 37° 27'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-4**2-17**2 }{ 2 * 17 * 4 } ) = 134° 18'33" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24.33 }{ 20.5 } = 1.19 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 8° 13'42" } = 13.97 ; ;




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