10 16 18 triangle

Acute scalene triangle.

Sides: a = 10   b = 16   c = 18

Area: T = 79.59989949685
Perimeter: p = 44
Semiperimeter: s = 22

Angle ∠ A = α = 33.55773097619° = 33°33'26″ = 0.58656855435 rad
Angle ∠ B = β = 62.18218607153° = 62°10'55″ = 1.08552782045 rad
Angle ∠ C = γ = 84.26108295227° = 84°15'39″ = 1.47106289056 rad

Height: ha = 15.92197989937
Height: hb = 9.95498743711
Height: hc = 8.84443327743

Median: ma = 16.27988205961
Median: mb = 12.16655250606
Median: mc = 9.84988578018

Inradius: r = 3.61881361349
Circumradius: R = 9.04553403373

Vertex coordinates: A[18; 0] B[0; 0] C[4.66766666667; 8.84443327743]
Centroid: CG[7.55655555556; 2.94881109248]
Coordinates of the circumscribed circle: U[9; 0.90545340337]
Coordinates of the inscribed circle: I[6; 3.61881361349]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4432690238° = 146°26'34″ = 0.58656855435 rad
∠ B' = β' = 117.8188139285° = 117°49'5″ = 1.08552782045 rad
∠ C' = γ' = 95.73991704773° = 95°44'21″ = 1.47106289056 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 = 16 ; ; c = 18 ; ;

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

p = a+b+c = 10+16+18 = 44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44 }{ 2 } = 22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22 * (22-10)(22-16)(22-18) } ; ; T = sqrt{ 6336 } = 79.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.6 }{ 10 } = 15.92 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.6 }{ 16 } = 9.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.6 }{ 18 } = 8.84 ; ;

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**2-16**2-18**2 }{ 2 * 16 * 18 } ) = 33° 33'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 16**2-10**2-18**2 }{ 2 * 10 * 18 } ) = 62° 10'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-10**2-16**2 }{ 2 * 16 * 10 } ) = 84° 15'39" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.6 }{ 22 } = 3.62 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 33° 33'26" } = 9.05 ; ;




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