7 22 24 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 22   c = 24

Area: T = 76.24659015292
Perimeter: p = 53
Semiperimeter: s = 26.5

Angle ∠ A = α = 16.78767398169° = 16°47'12″ = 0.29329838805 rad
Angle ∠ B = β = 65.18879583752° = 65°11'17″ = 1.13877445063 rad
Angle ∠ C = γ = 98.02553018079° = 98°1'31″ = 1.71108642668 rad

Height: ha = 21.78545432941
Height: hb = 6.93114455936
Height: hc = 6.35438251274

Median: ma = 22.7544120506
Median: mb = 13.83883525031
Median: mc = 11.06879718106

Inradius: r = 2.87772038313
Circumradius: R = 12.11986841715

Vertex coordinates: A[24; 0] B[0; 0] C[2.93875; 6.35438251274]
Centroid: CG[8.97991666667; 2.11879417091]
Coordinates of the circumscribed circle: U[12; -1.69218942187]
Coordinates of the inscribed circle: I[4.5; 2.87772038313]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.2133260183° = 163°12'48″ = 0.29329838805 rad
∠ B' = β' = 114.8122041625° = 114°48'43″ = 1.13877445063 rad
∠ C' = γ' = 81.97546981921° = 81°58'29″ = 1.71108642668 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 = 22 ; ; c = 24 ; ;

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

p = a+b+c = 7+22+24 = 53 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 53 }{ 2 } = 26.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26.5 * (26.5-7)(26.5-22)(26.5-24) } ; ; T = sqrt{ 5813.44 } = 76.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.25 }{ 7 } = 21.78 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.25 }{ 22 } = 6.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.25 }{ 24 } = 6.35 ; ;

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**2-22**2-24**2 }{ 2 * 22 * 24 } ) = 16° 47'12" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-7**2-24**2 }{ 2 * 7 * 24 } ) = 65° 11'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 24**2-7**2-22**2 }{ 2 * 22 * 7 } ) = 98° 1'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.25 }{ 26.5 } = 2.88 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 16° 47'12" } = 12.12 ; ;




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