11 15 22 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 15   c = 22

Area: T = 74.94399759808
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 27.01222939589° = 27°44″ = 0.47114534681 rad
Angle ∠ B = β = 38.26878548582° = 38°16'4″ = 0.6687900065 rad
Angle ∠ C = γ = 114.7219851183° = 114°43'11″ = 2.00222391205 rad

Height: ha = 13.62554501783
Height: hb = 9.99219967974
Height: hc = 6.81327250892

Median: ma = 18.00769431054
Median: mb = 15.69223548265
Median: mc = 7.21111025509

Inradius: r = 3.12224989992
Circumradius: R = 12.11096916315

Vertex coordinates: A[22; 0] B[0; 0] C[8.63663636364; 6.81327250892]
Centroid: CG[10.21221212121; 2.27109083631]
Coordinates of the circumscribed circle: U[11; -5.06440528641]
Coordinates of the inscribed circle: I[9; 3.12224989992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.9887706041° = 152°59'16″ = 0.47114534681 rad
∠ B' = β' = 141.7322145142° = 141°43'56″ = 0.6687900065 rad
∠ C' = γ' = 65.28801488171° = 65°16'49″ = 2.00222391205 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 = 15 ; ; c = 22 ; ;

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

p = a+b+c = 11+15+22 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-11)(24-15)(24-22) } ; ; T = sqrt{ 5616 } = 74.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 74.94 }{ 11 } = 13.63 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 74.94 }{ 15 } = 9.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 74.94 }{ 22 } = 6.81 ; ;

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**2-15**2-22**2 }{ 2 * 15 * 22 } ) = 27° 44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-11**2-22**2 }{ 2 * 11 * 22 } ) = 38° 16'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-11**2-15**2 }{ 2 * 15 * 11 } ) = 114° 43'11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 74.94 }{ 24 } = 3.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 27° 44" } = 12.11 ; ;




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