10 17 26 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 17   c = 26

Area: T = 45.5733429759
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 11.90106106561° = 11°54'2″ = 0.20877048389 rad
Angle ∠ B = β = 20.52218674° = 20°31'19″ = 0.35881741548 rad
Angle ∠ C = γ = 147.5787521944° = 147°34'39″ = 2.57657136599 rad

Height: ha = 9.11546859518
Height: hb = 5.36215799716
Height: hc = 3.5065648443

Median: ma = 21.38992496362
Median: mb = 17.76993556439
Median: mc = 5.05497524692

Inradius: r = 1.72197520664
Circumradius: R = 24.24765841575

Vertex coordinates: A[26; 0] B[0; 0] C[9.36553846154; 3.5065648443]
Centroid: CG[11.78884615385; 1.1698549481]
Coordinates of the circumscribed circle: U[13; -20.46769695683]
Coordinates of the inscribed circle: I[9.5; 1.72197520664]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.0999389344° = 168°5'58″ = 0.20877048389 rad
∠ B' = β' = 159.47881326° = 159°28'41″ = 0.35881741548 rad
∠ C' = γ' = 32.42224780561° = 32°25'21″ = 2.57657136599 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 = 10 ; ; b = 17 ; ; c = 26 ; ;

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

p = a+b+c = 10+17+26 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-10)(26.5-17)(26.5-26) } ; ; T = sqrt{ 2076.94 } = 45.57 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 45.57 }{ 10 } = 9.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 45.57 }{ 17 } = 5.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 45.57 }{ 26 } = 3.51 ; ;

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{ 10**2-17**2-26**2 }{ 2 * 17 * 26 } ) = 11° 54'2" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-10**2-26**2 }{ 2 * 10 * 26 } ) = 20° 31'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-10**2-17**2 }{ 2 * 17 * 10 } ) = 147° 34'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 45.57 }{ 26.5 } = 1.72 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 11° 54'2" } = 24.25 ; ;




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