7 15 18 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 15   c = 18

Area: T = 50.99901951359
Perimeter: p = 40
Semiperimeter: s = 20

Angle ∠ A = α = 22.19216065663° = 22°11'30″ = 0.38773166009 rad
Angle ∠ B = β = 54.03442464357° = 54°2'3″ = 0.94330755091 rad
Angle ∠ C = γ = 103.7744146998° = 103°46'27″ = 1.81112005436 rad

Height: ha = 14.56986271817
Height: hb = 6.79986926848
Height: hc = 5.66655772373

Median: ma = 16.19441347407
Median: mb = 11.41327122105
Median: mc = 7.48333147735

Inradius: r = 2.55495097568
Circumradius: R = 9.26664873853

Vertex coordinates: A[18; 0] B[0; 0] C[4.11111111111; 5.66655772373]
Centroid: CG[7.37703703704; 1.88985257458]
Coordinates of the circumscribed circle: U[9; -2.20663065203]
Coordinates of the inscribed circle: I[5; 2.55495097568]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.8088393434° = 157°48'30″ = 0.38773166009 rad
∠ B' = β' = 125.9665753564° = 125°57'57″ = 0.94330755091 rad
∠ C' = γ' = 76.2265853002° = 76°13'33″ = 1.81112005436 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 = 15 ; ; c = 18 ; ;

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

p = a+b+c = 7+15+18 = 40 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 40 }{ 2 } = 20 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20 * (20-7)(20-15)(20-18) } ; ; T = sqrt{ 2600 } = 50.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 50.99 }{ 7 } = 14.57 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 50.99 }{ 15 } = 6.8 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 50.99 }{ 18 } = 5.67 ; ;

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**2-15**2-18**2 }{ 2 * 15 * 18 } ) = 22° 11'30" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-7**2-18**2 }{ 2 * 7 * 18 } ) = 54° 2'3" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-7**2-15**2 }{ 2 * 15 * 7 } ) = 103° 46'27" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 50.99 }{ 20 } = 2.55 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 22° 11'30" } = 9.27 ; ;




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