4 5 8 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 5   c = 8

Area: T = 8.1821534086
Perimeter: p = 17
Semiperimeter: s = 8.5

Angle ∠ A = α = 24.14768479965° = 24°8'49″ = 0.42114420015 rad
Angle ∠ B = β = 30.75435198081° = 30°45'13″ = 0.53767501772 rad
Angle ∠ C = γ = 125.1099632195° = 125°5'59″ = 2.18334004748 rad

Height: ha = 4.0910767043
Height: hb = 3.27326136344
Height: hc = 2.04553835215

Median: ma = 6.36439610307
Median: mb = 5.80994750193
Median: mc = 2.12113203436

Inradius: r = 0.96325334219
Circumradius: R = 4.88990586508

Vertex coordinates: A[8; 0] B[0; 0] C[3.43875; 2.04553835215]
Centroid: CG[3.81325; 0.68217945072]
Coordinates of the circumscribed circle: U[4; -2.81112087242]
Coordinates of the inscribed circle: I[3.5; 0.96325334219]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.8533152003° = 155°51'11″ = 0.42114420015 rad
∠ B' = β' = 149.2466480192° = 149°14'47″ = 0.53767501772 rad
∠ C' = γ' = 54.99003678046° = 54°54'1″ = 2.18334004748 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 = 4 ; ; b = 5 ; ; c = 8 ; ;

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

p = a+b+c = 4+5+8 = 17 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17 }{ 2 } = 8.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.5 * (8.5-4)(8.5-5)(8.5-8) } ; ; T = sqrt{ 66.94 } = 8.18 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 8.18 }{ 4 } = 4.09 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 8.18 }{ 5 } = 3.27 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 8.18 }{ 8 } = 2.05 ; ;

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**2-5**2-8**2 }{ 2 * 5 * 8 } ) = 24° 8'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5**2-4**2-8**2 }{ 2 * 4 * 8 } ) = 30° 45'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8**2-4**2-5**2 }{ 2 * 5 * 4 } ) = 125° 5'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 8.18 }{ 8.5 } = 0.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 24° 8'49" } = 4.89 ; ;




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