4 15 18 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 15   c = 18

Area: T = 21.66765064097
Perimeter: p = 37
Semiperimeter: s = 18.5

Angle ∠ A = α = 9.23554919597° = 9°14'8″ = 0.16111897427 rad
Angle ∠ B = β = 37.00223228374° = 37°8″ = 0.64658123644 rad
Angle ∠ C = γ = 133.7622185203° = 133°45'44″ = 2.33545905465 rad

Height: ha = 10.83332532048
Height: hb = 2.88988675213
Height: hc = 2.40773896011

Median: ma = 16.44768842034
Median: mb = 10.66553645039
Median: mc = 6.2854902545

Inradius: r = 1.17111625086
Circumradius: R = 12.46216306337

Vertex coordinates: A[18; 0] B[0; 0] C[3.19444444444; 2.40773896011]
Centroid: CG[7.06548148148; 0.80224632004]
Coordinates of the circumscribed circle: U[9; -8.61992945216]
Coordinates of the inscribed circle: I[3.5; 1.17111625086]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 170.765450804° = 170°45'52″ = 0.16111897427 rad
∠ B' = β' = 142.9987677163° = 142°59'52″ = 0.64658123644 rad
∠ C' = γ' = 46.23878147971° = 46°14'16″ = 2.33545905465 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 = 4 ; ; b = 15 ; ; c = 18 ; ;

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

p = a+b+c = 4+15+18 = 37 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 37 }{ 2 } = 18.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 18.5 * (18.5-4)(18.5-15)(18.5-18) } ; ; T = sqrt{ 469.44 } = 21.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 21.67 }{ 4 } = 10.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 21.67 }{ 15 } = 2.89 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 21.67 }{ 18 } = 2.41 ; ;

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{ 4**2-15**2-18**2 }{ 2 * 15 * 18 } ) = 9° 14'8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-4**2-18**2 }{ 2 * 4 * 18 } ) = 37° 8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-4**2-15**2 }{ 2 * 15 * 4 } ) = 133° 45'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 21.67 }{ 18.5 } = 1.17 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 9° 14'8" } = 12.46 ; ;




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