10 15 22 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 15   c = 22

Area: T = 63.6599823113
Perimeter: p = 47
Semiperimeter: s = 23.5

Angle ∠ A = α = 22.67218953288° = 22°40'19″ = 0.39656992212 rad
Angle ∠ B = β = 35.32326498434° = 35°19'22″ = 0.61664965403 rad
Angle ∠ C = γ = 122.0055454828° = 122°20″ = 2.12993968921 rad

Height: ha = 12.72199646226
Height: hb = 8.48799764151
Height: hc = 5.78218021012

Median: ma = 18.15221348607
Median: mb = 15.35441525328
Median: mc = 6.44220493634

Inradius: r = 2.70663754516
Circumradius: R = 12.97217341907

Vertex coordinates: A[22; 0] B[0; 0] C[8.15990909091; 5.78218021012]
Centroid: CG[10.0533030303; 1.92772673671]
Coordinates of the circumscribed circle: U[11; -6.87550191211]
Coordinates of the inscribed circle: I[8.5; 2.70663754516]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.3288104671° = 157°19'41″ = 0.39656992212 rad
∠ B' = β' = 144.6777350157° = 144°40'38″ = 0.61664965403 rad
∠ C' = γ' = 57.99545451722° = 57°59'40″ = 2.12993968921 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 = 15 ; ; c = 22 ; ;

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

p = a+b+c = 10+15+22 = 47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 47 }{ 2 } = 23.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.5 * (23.5-10)(23.5-15)(23.5-22) } ; ; T = sqrt{ 4044.94 } = 63.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 63.6 }{ 10 } = 12.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 63.6 }{ 15 } = 8.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 63.6 }{ 22 } = 5.78 ; ;

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**2-15**2-22**2 }{ 2 * 15 * 22 } ) = 22° 40'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-10**2-22**2 }{ 2 * 10 * 22 } ) = 35° 19'22" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-10**2-15**2 }{ 2 * 15 * 10 } ) = 122° 20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 63.6 }{ 23.5 } = 2.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 22° 40'19" } = 12.97 ; ;




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