11 16 25 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 16   c = 25

Area: T = 62.4549979984
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 27.01222939589° = 27°44″ = 0.47114534681 rad
Angle ∠ C = γ = 134.7932833702° = 134°47'34″ = 2.35325787562 rad

Height: ha = 11.35545418153
Height: hb = 7.8066247498
Height: hc = 4.99659983987

Median: ma = 20.25546291005
Median: mb = 17.57883958312
Median: mc = 5.67989083458

Inradius: r = 2.40219223071
Circumradius: R = 17.61440969186

Vertex coordinates: A[25; 0] B[0; 0] C[9.8; 4.99659983987]
Centroid: CG[11.6; 1.66553327996]
Coordinates of the circumscribed circle: U[12.5; -12.41099319199]
Coordinates of the inscribed circle: I[10; 2.40219223071]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 152.9887706041° = 152°59'16″ = 0.47114534681 rad
∠ C' = γ' = 45.20771662976° = 45°12'26″ = 2.35325787562 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 = 11 ; ; b = 16 ; ; c = 25 ; ;

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

p = a+b+c = 11+16+25 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-11)(26-16)(26-25) } ; ; T = sqrt{ 3900 } = 62.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.45 }{ 11 } = 11.35 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.45 }{ 16 } = 7.81 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.45 }{ 25 } = 5 ; ;

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{ 11**2-16**2-25**2 }{ 2 * 16 * 25 } ) = 18° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-11**2-25**2 }{ 2 * 11 * 25 } ) = 27° 44" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-11**2-16**2 }{ 2 * 16 * 11 } ) = 134° 47'34" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.45 }{ 26 } = 2.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 18° 11'42" } = 17.61 ; ;




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