16 20 26 triangle

Obtuse scalene triangle.

Sides: a = 16   b = 20   c = 26

Area: T = 159.9221855917
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 37.95880285807° = 37°57'29″ = 0.66224925763 rad
Angle ∠ B = β = 50.251118676° = 50°15'4″ = 0.8777048662 rad
Angle ∠ C = γ = 91.79107846593° = 91°47'27″ = 1.60220514153 rad

Height: ha = 19.99902319896
Height: hb = 15.99221855917
Height: hc = 12.30216812244

Median: ma = 21.77215410571
Median: mb = 19.13111264697
Median: mc = 12.61095202129

Inradius: r = 5.15987695457
Circumradius: R = 13.00663523092

Vertex coordinates: A[26; 0] B[0; 0] C[10.23107692308; 12.30216812244]
Centroid: CG[12.07769230769; 4.10105604081]
Coordinates of the circumscribed circle: U[13; -0.40664485097]
Coordinates of the inscribed circle: I[11; 5.15987695457]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0421971419° = 142°2'31″ = 0.66224925763 rad
∠ B' = β' = 129.749881324° = 129°44'56″ = 0.8777048662 rad
∠ C' = γ' = 88.20992153407° = 88°12'33″ = 1.60220514153 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 = 20 ; ; c = 26 ; ;

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

p = a+b+c = 16+20+26 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-16)(31-20)(31-26) } ; ; T = sqrt{ 25575 } = 159.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 159.92 }{ 16 } = 19.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 159.92 }{ 20 } = 15.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 159.92 }{ 26 } = 12.3 ; ;

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**2-20**2-26**2 }{ 2 * 20 * 26 } ) = 37° 57'29" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 50° 15'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-16**2-20**2 }{ 2 * 20 * 16 } ) = 91° 47'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 159.92 }{ 31 } = 5.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 37° 57'29" } = 13.01 ; ;




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