14 15 22 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 15   c = 22

Area: T = 103.812202965
Perimeter: p = 51
Semiperimeter: s = 25.5

Angle ∠ A = α = 38.98884573105° = 38°59'18″ = 0.68804769503 rad
Angle ∠ B = β = 42.38546161308° = 42°23'5″ = 0.74397511037 rad
Angle ∠ C = γ = 98.62769265587° = 98°37'37″ = 1.72113645996 rad

Height: ha = 14.833028995
Height: hb = 13.84216039533
Height: hc = 9.43774572409

Median: ma = 17.47985582929
Median: mb = 16.84548805279
Median: mc = 9.46604439642

Inradius: r = 4.07110599863
Circumradius: R = 11.12658782233

Vertex coordinates: A[22; 0] B[0; 0] C[10.34109090909; 9.43774572409]
Centroid: CG[10.78803030303; 3.14658190803]
Coordinates of the circumscribed circle: U[11; -1.66988817335]
Coordinates of the inscribed circle: I[10.5; 4.07110599863]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 141.0121542689° = 141°42″ = 0.68804769503 rad
∠ B' = β' = 137.6155383869° = 137°36'55″ = 0.74397511037 rad
∠ C' = γ' = 81.37330734413° = 81°22'23″ = 1.72113645996 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 = 14 ; ; b = 15 ; ; c = 22 ; ;

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

p = a+b+c = 14+15+22 = 51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 51 }{ 2 } = 25.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 25.5 * (25.5-14)(25.5-15)(25.5-22) } ; ; T = sqrt{ 10776.94 } = 103.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 103.81 }{ 14 } = 14.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 103.81 }{ 15 } = 13.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 103.81 }{ 22 } = 9.44 ; ;

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{ 14**2-15**2-22**2 }{ 2 * 15 * 22 } ) = 38° 59'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-14**2-22**2 }{ 2 * 14 * 22 } ) = 42° 23'5" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 22**2-14**2-15**2 }{ 2 * 15 * 14 } ) = 98° 37'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 103.81 }{ 25.5 } = 4.07 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 38° 59'18" } = 11.13 ; ;




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