7 22 23 triangle

Acute scalene triangle.

Sides: a = 7   b = 22   c = 23

Area: T = 76.99435062197
Perimeter: p = 52
Semiperimeter: s = 26

Angle ∠ A = α = 17.71773880236° = 17°43'3″ = 0.30992267559 rad
Angle ∠ B = β = 73.02767339276° = 73°1'36″ = 1.2754556949 rad
Angle ∠ C = γ = 89.25658780488° = 89°15'21″ = 1.55878089487 rad

Height: ha = 21.99881446342
Height: hb = 6.99994096563
Height: hc = 6.69550874974

Median: ma = 22.23217340754
Median: mb = 12.96114813968
Median: mc = 11.58766302263

Inradius: r = 2.96112887008
Circumradius: R = 11.50109699321

Vertex coordinates: A[23; 0] B[0; 0] C[2.04334782609; 6.69550874974]
Centroid: CG[8.3487826087; 2.23216958325]
Coordinates of the circumscribed circle: U[11.5; 0.14993632459]
Coordinates of the inscribed circle: I[4; 2.96112887008]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 162.2832611976° = 162°16'57″ = 0.30992267559 rad
∠ B' = β' = 106.9733266072° = 106°58'24″ = 1.2754556949 rad
∠ C' = γ' = 90.74441219512° = 90°44'39″ = 1.55878089487 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 = 23 ; ;

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

p = a+b+c = 7+22+23 = 52 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 52 }{ 2 } = 26 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 26 * (26-7)(26-22)(26-23) } ; ; T = sqrt{ 5928 } = 76.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 76.99 }{ 7 } = 22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 76.99 }{ 22 } = 7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 76.99 }{ 23 } = 6.7 ; ;

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**2-23**2 }{ 2 * 22 * 23 } ) = 17° 43'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 22**2-7**2-23**2 }{ 2 * 7 * 23 } ) = 73° 1'36" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 23**2-7**2-22**2 }{ 2 * 22 * 7 } ) = 89° 15'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 76.99 }{ 26 } = 2.96 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 17° 43'3" } = 11.5 ; ;




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