17 18 30 triangle

Obtuse scalene triangle.

Sides: a = 17   b = 18   c = 30

Area: T = 135.1333036301
Perimeter: p = 65
Semiperimeter: s = 32.5

Angle ∠ A = α = 30.03326039163° = 30°1'57″ = 0.52441678213 rad
Angle ∠ B = β = 32.00109601588° = 32°3″ = 0.55985221186 rad
Angle ∠ C = γ = 117.9666435925° = 117°57'59″ = 2.05989027137 rad

Height: ha = 15.89880042707
Height: hb = 15.01547818113
Height: hc = 9.00988690868

Median: ma = 23.2332520311
Median: mb = 22.66105383872
Median: mc = 9.02877350426

Inradius: r = 4.15879395785
Circumradius: R = 16.98332637734

Vertex coordinates: A[30; 0] B[0; 0] C[14.41766666667; 9.00988690868]
Centroid: CG[14.80655555556; 3.00329563623]
Coordinates of the circumscribed circle: U[15; -7.96443736976]
Coordinates of the inscribed circle: I[14.5; 4.15879395785]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 149.9677396084° = 149°58'3″ = 0.52441678213 rad
∠ B' = β' = 147.9999039841° = 147°59'57″ = 0.55985221186 rad
∠ C' = γ' = 62.0343564075° = 62°2'1″ = 2.05989027137 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 = 17 ; ; b = 18 ; ; c = 30 ; ;

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

p = a+b+c = 17+18+30 = 65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 65 }{ 2 } = 32.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 32.5 * (32.5-17)(32.5-18)(32.5-30) } ; ; T = sqrt{ 18260.94 } = 135.13 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 135.13 }{ 17 } = 15.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 135.13 }{ 18 } = 15.01 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 135.13 }{ 30 } = 9.01 ; ;

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{ 17**2-18**2-30**2 }{ 2 * 18 * 30 } ) = 30° 1'57" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-17**2-30**2 }{ 2 * 17 * 30 } ) = 32° 3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-17**2-18**2 }{ 2 * 18 * 17 } ) = 117° 57'59" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 135.13 }{ 32.5 } = 4.16 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 17 }{ 2 * sin 30° 1'57" } = 16.98 ; ;




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