7 18 20 triangle

Obtuse scalene triangle.

Sides: a = 7 b = 18 c = 20

Area: T = 62.63773490818
Perimeter: p = 45
Semiperimeter: s = 22.5

Angle ∠ A = α = 20.36441348063° = 20°21'51″ = 0.35554212017 rad
Angle ∠ B = β = 63.48552253657° = 63°29'7″ = 1.1088026209 rad
Angle ∠ C = γ = 96.15106398279° = 96°9'2″ = 1.67881452429 rad

Height: h_a = 17.8966385452
Height: h_b = 6.96597054535
Height: h_c = 6.26437349082

Median: m_a = 18.70216042093
Median: m_b = 11.97991485507
Median: m_c = 9.30105376189

Inradius: r = 2.78438821814
Circumradius: R = 10.05878969135

Vertex coordinates: A[20; 0] B[0; 0] C[3.125; 6.26437349082]
Centroid: CG[7.70883333333; 2.08879116361]
Coordinates of the circumscribed circle: U[10; -1.07876318122]
Coordinates of the inscribed circle: I[4.5; 2.78438821814]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 159.6365865194° = 159°38'9″ = 0.35554212017 rad
∠ B' = β' = 116.5154774634° = 116°30'53″ = 1.1088026209 rad
∠ C' = γ' = 83.84993601721° = 83°50'58″ = 1.67881452429 rad

Calculate another triangle

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.

$a = 7 ; ; b = 18 ; ; c = 20 ; ;$

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

$p = a+b+c = 7+18+20 = 45 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 45 }{ 2 } = 22.5 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.5 * (22.5-7)(22.5-18)(22.5-20) } ; ; T = sqrt{ 3923.44 } = 62.64 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 62.64 }{ 7 } = 17.9 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 62.64 }{ 18 } = 6.96 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 62.64 }{ 20 } = 6.26 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 7**2-18**2-20**2 }{ 2 * 18 * 20 } ) = 20° 21'51" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 18**2-7**2-20**2 }{ 2 * 7 * 20 } ) = 63° 29'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 20**2-7**2-18**2 }{ 2 * 18 * 7 } ) = 96° 9'2" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 62.64 }{ 22.5 } = 2.78 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 20° 21'51" } = 10.06 ; ;$

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