22 26 30 triangle

Acute scalene triangle.

Sides: a = 22   b = 26   c = 30

Area: T = 278.5165708713
Perimeter: p = 78
Semiperimeter: s = 39

Angle ∠ A = α = 45.57329959992° = 45°34'23″ = 0.79553988302 rad
Angle ∠ B = β = 57.56435627878° = 57°33'49″ = 1.00546736998 rad
Angle ∠ C = γ = 76.86334412131° = 76°51'48″ = 1.34215201236 rad

Height: ha = 25.3219609883
Height: hb = 21.42442852856
Height: hc = 18.56877139142

Median: ma = 25.82663431403
Median: mb = 22.86991932521
Median: mc = 18.84114436814

Inradius: r = 7.14114284285
Circumradius: R = 15.40330809243

Vertex coordinates: A[30; 0] B[0; 0] C[11.8; 18.56877139142]
Centroid: CG[13.93333333333; 6.18992379714]
Coordinates of the circumscribed circle: U[15; 3.50107002101]
Coordinates of the inscribed circle: I[13; 7.14114284285]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.4277004001° = 134°25'37″ = 0.79553988302 rad
∠ B' = β' = 122.4366437212° = 122°26'11″ = 1.00546736998 rad
∠ C' = γ' = 103.1376558787° = 103°8'12″ = 1.34215201236 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 = 22 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 22+26+30 = 78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 78 }{ 2 } = 39 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 39 * (39-22)(39-26)(39-30) } ; ; T = sqrt{ 77571 } = 278.52 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 278.52 }{ 22 } = 25.32 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 278.52 }{ 26 } = 21.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 278.52 }{ 30 } = 18.57 ; ;

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{ 22**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 45° 34'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-22**2-30**2 }{ 2 * 22 * 30 } ) = 57° 33'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-22**2-26**2 }{ 2 * 26 * 22 } ) = 76° 51'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 278.52 }{ 39 } = 7.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 22 }{ 2 * sin 45° 34'23" } = 15.4 ; ;




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