15 16 26 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 16   c = 26

Area: T = 109.6511436379
Perimeter: p = 57
Semiperimeter: s = 28.5

Angle ∠ A = α = 31.81444665509° = 31°48'52″ = 0.55552671911 rad
Angle ∠ B = β = 34.21660511313° = 34°12'58″ = 0.59771827493 rad
Angle ∠ C = γ = 113.9699482318° = 113°58'10″ = 1.98991427132 rad

Height: ha = 14.62201915172
Height: hb = 13.70664295474
Height: hc = 8.43547258753

Median: ma = 20.242228248
Median: mb = 19.66596032513
Median: mc = 8.45657672626

Inradius: r = 3.84774188203
Circumradius: R = 14.22768998156

Vertex coordinates: A[26; 0] B[0; 0] C[12.40438461538; 8.43547258753]
Centroid: CG[12.80112820513; 2.81215752918]
Coordinates of the circumscribed circle: U[13; -5.78796780501]
Coordinates of the inscribed circle: I[12.5; 3.84774188203]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 148.1865533449° = 148°11'8″ = 0.55552671911 rad
∠ B' = β' = 145.7843948869° = 145°47'2″ = 0.59771827493 rad
∠ C' = γ' = 66.03105176822° = 66°1'50″ = 1.98991427132 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 = 15 ; ; b = 16 ; ; c = 26 ; ;

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

p = a+b+c = 15+16+26 = 57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 57 }{ 2 } = 28.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 28.5 * (28.5-15)(28.5-16)(28.5-26) } ; ; T = sqrt{ 12023.44 } = 109.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 109.65 }{ 15 } = 14.62 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 109.65 }{ 16 } = 13.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 109.65 }{ 26 } = 8.43 ; ;

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{ 15**2-16**2-26**2 }{ 2 * 16 * 26 } ) = 31° 48'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-15**2-26**2 }{ 2 * 15 * 26 } ) = 34° 12'58" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 26**2-15**2-16**2 }{ 2 * 16 * 15 } ) = 113° 58'10" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 109.65 }{ 28.5 } = 3.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 31° 48'52" } = 14.23 ; ;




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