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: ha = 17.8966385452
Height: hb = 6.96597054535
Height: hc = 6.26437349082

Median: ma = 18.70216042093
Median: mb = 11.97991485507
Median: mc = 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

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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 = 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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 18**2+20**2-7**2 }{ 2 * 18 * 20 } ) = 20° 21'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+20**2-18**2 }{ 2 * 7 * 20 } ) = 63° 29'7" ; ; gamma = 180° - alpha - beta = 180° - 20° 21'51" - 63° 29'7" = 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 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 20**2 - 7**2 } }{ 2 } = 18.702 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 20**2+2 * 7**2 - 18**2 } }{ 2 } = 11.979 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 7**2 - 20**2 } }{ 2 } = 9.301 ; ;
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