14 16 18 triangle

Acute scalene triangle.

Sides: a = 14   b = 16   c = 18

Area: T = 107.331126292
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 48.19896851042° = 48°11'23″ = 0.84110686706 rad
Angle ∠ B = β = 58.41218644948° = 58°24'43″ = 1.01994793577 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: ha = 15.333303756
Height: hb = 13.4166407865
Height: hc = 11.926569588

Median: ma = 15.52441746963
Median: mb = 14
Median: mc = 12.04215945788

Inradius: r = 4.4722135955
Circumradius: R = 9.39114855055

Vertex coordinates: A[18; 0] B[0; 0] C[7.33333333333; 11.926569588]
Centroid: CG[8.44444444444; 3.975523196]
Coordinates of the circumscribed circle: U[9; 2.6833281573]
Coordinates of the inscribed circle: I[8; 4.4722135955]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 131.8110314896° = 131°48'37″ = 0.84110686706 rad
∠ B' = β' = 121.5888135505° = 121°35'17″ = 1.01994793577 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 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 = 16 ; ; c = 18 ; ;

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

p = a+b+c = 14+16+18 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-14)(24-16)(24-18) } ; ; T = sqrt{ 11520 } = 107.33 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 107.33 }{ 14 } = 15.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 107.33 }{ 16 } = 13.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 107.33 }{ 18 } = 11.93 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 16**2+18**2-14**2 }{ 2 * 16 * 18 } ) = 48° 11'23" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 14**2+18**2-16**2 }{ 2 * 14 * 18 } ) = 58° 24'43" ; ; gamma = 180° - alpha - beta = 180° - 48° 11'23" - 58° 24'43" = 73° 23'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 107.33 }{ 24 } = 4.47 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 14 }{ 2 * sin 48° 11'23" } = 9.39 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 18**2 - 14**2 } }{ 2 } = 15.524 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 14**2 - 16**2 } }{ 2 } = 14 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 14**2 - 18**2 } }{ 2 } = 12.042 ; ;
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