8 10 16 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 10   c = 16

Area: T = 32.72661363439
Perimeter: p = 34
Semiperimeter: s = 17

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 = 8.1821534086
Height: hb = 6.54552272688
Height: hc = 4.0910767043

Median: ma = 12.72879220614
Median: mb = 11.61989500386
Median: mc = 4.24326406871

Inradius: r = 1.92550668438
Circumradius: R = 9.77881173016

Vertex coordinates: A[16; 0] B[0; 0] C[6.875; 4.0910767043]
Centroid: CG[7.625; 1.36435890143]
Coordinates of the circumscribed circle: U[8; -5.62224174484]
Coordinates of the inscribed circle: I[7; 1.92550668438]

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 = 8 ; ; b = 10 ; ; c = 16 ; ;

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

p = a+b+c = 8+10+16 = 34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34 }{ 2 } = 17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17 * (17-8)(17-10)(17-16) } ; ; T = sqrt{ 1071 } = 32.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 32.73 }{ 8 } = 8.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 32.73 }{ 10 } = 6.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 32.73 }{ 16 } = 4.09 ; ;

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{ 8**2-10**2-16**2 }{ 2 * 10 * 16 } ) = 24° 8'49" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-8**2-16**2 }{ 2 * 8 * 16 } ) = 30° 45'13" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 16**2-8**2-10**2 }{ 2 * 10 * 8 } ) = 125° 5'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 32.73 }{ 17 } = 1.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 24° 8'49" } = 9.78 ; ;




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