10 17 18 triangle

Acute scalene triangle.

Sides: a = 10   b = 17   c = 18

Area: T = 83.43222329798
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 33.04657624726° = 33°2'45″ = 0.5776757359 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 78.97985503645° = 78°58'43″ = 1.37884357423 rad

Height: ha = 16.6866446596
Height: hb = 9.81655568212
Height: hc = 9.27702481089

Median: ma = 16.77879617356
Median: mb = 11.82215904175
Median: mc = 10.65436378763

Inradius: r = 3.70880992435
Circumradius: R = 9.16991181295

Vertex coordinates: A[18; 0] B[0; 0] C[3.75; 9.27702481089]
Centroid: CG[7.25; 3.0990082703]
Coordinates of the circumscribed circle: U[9; 1.75329196424]
Coordinates of the inscribed circle: I[5.5; 3.70880992435]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9544237527° = 146°57'15″ = 0.5776757359 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 101.0211449636° = 101°1'17″ = 1.37884357423 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 = 10 ; ; b = 17 ; ; c = 18 ; ;

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

p = a+b+c = 10+17+18 = 45 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-10)(22.5-17)(22.5-18) } ; ; T = sqrt{ 6960.94 } = 83.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 83.43 }{ 10 } = 16.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 83.43 }{ 17 } = 9.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 83.43 }{ 18 } = 9.27 ; ;

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{ 10**2-17**2-18**2 }{ 2 * 17 * 18 } ) = 33° 2'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 17**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-17**2 }{ 2 * 17 * 10 } ) = 78° 58'43" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 83.43 }{ 22.5 } = 3.71 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 33° 2'45" } = 9.17 ; ;




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