7 20 22 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 20   c = 22

Area: T = 69.45109719154
Perimeter: p = 49
Semiperimeter: s = 24.5

Angle ∠ A = α = 18.40222461959° = 18°24'8″ = 0.32111797859 rad
Angle ∠ B = β = 64.41769980226° = 64°25'1″ = 1.12442887097 rad
Angle ∠ C = γ = 97.18107557815° = 97°10'51″ = 1.6966124158 rad

Height: ha = 19.8433134833
Height: hb = 6.94550971915
Height: hc = 6.31437247196

Median: ma = 20.73304124416
Median: mb = 12.90334879006
Median: mc = 10.17334949747

Inradius: r = 2.83547335476
Circumradius: R = 11.08769578749

Vertex coordinates: A[22; 0] B[0; 0] C[3.02327272727; 6.31437247196]
Centroid: CG[8.34109090909; 2.10545749065]
Coordinates of the circumscribed circle: U[11; -1.38658697344]
Coordinates of the inscribed circle: I[4.5; 2.83547335476]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.5987753804° = 161°35'52″ = 0.32111797859 rad
∠ B' = β' = 115.5833001977° = 115°34'59″ = 1.12442887097 rad
∠ C' = γ' = 82.81992442185° = 82°49'9″ = 1.6966124158 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 = 7 ; ; b = 20 ; ; c = 22 ; ;

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

p = a+b+c = 7+20+22 = 49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49 }{ 2 } = 24.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.5 * (24.5-7)(24.5-20)(24.5-22) } ; ; T = sqrt{ 4823.44 } = 69.45 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 69.45 }{ 7 } = 19.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 69.45 }{ 20 } = 6.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 69.45 }{ 22 } = 6.31 ; ;

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{ 7**2-20**2-22**2 }{ 2 * 20 * 22 } ) = 18° 24'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-7**2-22**2 }{ 2 * 7 * 22 } ) = 64° 25'1" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-7**2-20**2 }{ 2 * 20 * 7 } ) = 97° 10'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 69.45 }{ 24.5 } = 2.83 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 18° 24'8" } = 11.09 ; ;




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