8 15 18 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 15   c = 18

Area: T = 59.35985503529
Perimeter: p = 41
Semiperimeter: s = 20.5

Angle ∠ A = α = 26.08442927774° = 26°5'3″ = 0.4555256792 rad
Angle ∠ B = β = 55.53301685755° = 55°31'49″ = 0.96991842758 rad
Angle ∠ C = γ = 98.38655386471° = 98°23'8″ = 1.71771515857 rad

Height: ha = 14.84396375882
Height: hb = 7.91444733804
Height: hc = 6.59553944837

Median: ma = 16.07879351908
Median: mb = 11.73766945943
Median: mc = 7.96986887253

Inradius: r = 2.89655390416
Circumradius: R = 9.09772572071

Vertex coordinates: A[18; 0] B[0; 0] C[4.52877777778; 6.59553944837]
Centroid: CG[7.50992592593; 2.19884648279]
Coordinates of the circumscribed circle: U[9; -1.32766833427]
Coordinates of the inscribed circle: I[5.5; 2.89655390416]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 153.9165707223° = 153°54'57″ = 0.4555256792 rad
∠ B' = β' = 124.4769831424° = 124°28'11″ = 0.96991842758 rad
∠ C' = γ' = 81.61444613529° = 81°36'52″ = 1.71771515857 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 = 8 ; ; b = 15 ; ; c = 18 ; ;

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

p = a+b+c = 8+15+18 = 41 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 41 }{ 2 } = 20.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 20.5 * (20.5-8)(20.5-15)(20.5-18) } ; ; T = sqrt{ 3523.44 } = 59.36 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 59.36 }{ 8 } = 14.84 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 59.36 }{ 15 } = 7.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 59.36 }{ 18 } = 6.6 ; ;

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{ 8**2-15**2-18**2 }{ 2 * 15 * 18 } ) = 26° 5'3" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15**2-8**2-18**2 }{ 2 * 8 * 18 } ) = 55° 31'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 18**2-8**2-15**2 }{ 2 * 15 * 8 } ) = 98° 23'8" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 59.36 }{ 20.5 } = 2.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 26° 5'3" } = 9.1 ; ;




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