5 22 25 triangle

Obtuse scalene triangle.

Sides: a = 5   b = 22   c = 25

Area: T = 46.73332857822
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 9.78442852588° = 9°47'3″ = 0.17107679927 rad
Angle ∠ B = β = 48.39443462161° = 48°23'40″ = 0.84546406808 rad
Angle ∠ C = γ = 121.8211368525° = 121°49'17″ = 2.126618398 rad

Height: ha = 18.69333143129
Height: hb = 4.24884805257
Height: hc = 3.73986628626

Median: ma = 23.41547389479
Median: mb = 14.28328568571
Median: mc = 9.91221138008

Inradius: r = 1.79774340685
Circumradius: R = 14.71111419301

Vertex coordinates: A[25; 0] B[0; 0] C[3.32; 3.73986628626]
Centroid: CG[9.44; 1.24662209542]
Coordinates of the circumscribed circle: U[12.5; -7.75767839268]
Coordinates of the inscribed circle: I[4; 1.79774340685]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.2165714741° = 170°12'57″ = 0.17107679927 rad
∠ B' = β' = 131.6065653784° = 131°36'20″ = 0.84546406808 rad
∠ C' = γ' = 58.17986314749° = 58°10'43″ = 2.126618398 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 = 5 ; ; b = 22 ; ; c = 25 ; ;

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

p = a+b+c = 5+22+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 * (26-5)(26-22)(26-25) } ; ; T = sqrt{ 2184 } = 46.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 46.73 }{ 5 } = 18.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 46.73 }{ 22 } = 4.25 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 46.73 }{ 25 } = 3.74 ; ;

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{ 5**2-22**2-25**2 }{ 2 * 22 * 25 } ) = 9° 47'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-5**2-25**2 }{ 2 * 5 * 25 } ) = 48° 23'40" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 25**2-5**2-22**2 }{ 2 * 22 * 5 } ) = 121° 49'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 46.73 }{ 26 } = 1.8 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5 }{ 2 * sin 9° 47'3" } = 14.71 ; ;




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