16 19 26 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 19   c = 26

Area: T = 151.2832641106
Perimeter: p = 61
Semiperimeter: s = 30.5

Angle ∠ A = α = 37.76990637407° = 37°46'9″ = 0.65991945177 rad
Angle ∠ B = β = 46.66222207563° = 46°39'44″ = 0.81444093885 rad
Angle ∠ C = γ = 95.56987155029° = 95°34'7″ = 1.66879887474 rad

Height: ha = 18.91103301382
Height: hb = 15.92444885375
Height: hc = 11.63771262389

Median: ma = 21.31990056053
Median: mb = 19.3844271975
Median: mc = 11.8111011811

Inradius: r = 4.96600865936
Circumradius: R = 13.062164399

Vertex coordinates: A[26; 0] B[0; 0] C[10.98107692308; 11.63771262389]
Centroid: CG[12.32769230769; 3.87990420796]
Coordinates of the circumscribed circle: U[13; -1.26774950582]
Coordinates of the inscribed circle: I[11.5; 4.96600865936]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.2310936259° = 142°13'51″ = 0.65991945177 rad
∠ B' = β' = 133.3387779244° = 133°20'16″ = 0.81444093885 rad
∠ C' = γ' = 84.43112844971° = 84°25'53″ = 1.66879887474 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 = 16 ; ; b = 19 ; ; c = 26 ; ;

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

p = a+b+c = 16+19+26 = 61 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61 }{ 2 } = 30.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.5 * (30.5-16)(30.5-19)(30.5-26) } ; ; T = sqrt{ 22886.44 } = 151.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 151.28 }{ 16 } = 18.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 151.28 }{ 19 } = 15.92 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 151.28 }{ 26 } = 11.64 ; ;

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{ 16**2-19**2-26**2 }{ 2 * 19 * 26 } ) = 37° 46'9" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 19**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 46° 39'44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-19**2 }{ 2 * 19 * 16 } ) = 95° 34'7" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 151.28 }{ 30.5 } = 4.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 37° 46'9" } = 13.06 ; ;




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