7 18 18 triangle

Acute isosceles triangle.

Sides: a = 7   b = 18   c = 18

Area: T = 61.79875525405
Perimeter: p = 43
Semiperimeter: s = 21.5

Angle ∠ A = α = 22.42545428353° = 22°25'28″ = 0.39113821057 rad
Angle ∠ B = β = 78.78877285824° = 78°47'16″ = 1.37551052739 rad
Angle ∠ C = γ = 78.78877285824° = 78°47'16″ = 1.37551052739 rad

Height: ha = 17.6566443583
Height: hb = 6.86663947267
Height: hc = 6.86663947267

Median: ma = 17.6566443583
Median: mb = 10.27113192921
Median: mc = 10.27113192921

Inradius: r = 2.87443047693
Circumradius: R = 9.1755120643

Vertex coordinates: A[18; 0] B[0; 0] C[1.36111111111; 6.86663947267]
Centroid: CG[6.45437037037; 2.28987982422]
Coordinates of the circumscribed circle: U[9; 1.78440512361]
Coordinates of the inscribed circle: I[3.5; 2.87443047693]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.5755457165° = 157°34'32″ = 0.39113821057 rad
∠ B' = β' = 101.2122271418° = 101°12'44″ = 1.37551052739 rad
∠ C' = γ' = 101.2122271418° = 101°12'44″ = 1.37551052739 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 = 18 ; ;

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

p = a+b+c = 7+18+18 = 43 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 43 }{ 2 } = 21.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.5 * (21.5-7)(21.5-18)(21.5-18) } ; ; T = sqrt{ 3818.94 } = 61.8 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 61.8 }{ 7 } = 17.66 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 61.8 }{ 18 } = 6.87 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 61.8 }{ 18 } = 6.87 ; ;

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+18**2-7**2 }{ 2 * 18 * 18 } ) = 22° 25'28" ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+18**2-18**2 }{ 2 * 7 * 18 } ) = 78° 47'16" ; ; gamma = arccos( fraction{ a**2+b**2-c**2 }{ 2ab } ) = arccos( fraction{ 7**2+18**2-18**2 }{ 2 * 7 * 18 } ) = 78° 47'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 61.8 }{ 21.5 } = 2.87 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 22° 25'28" } = 9.18 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 18**2 - 7**2 } }{ 2 } = 17.656 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 7**2 - 18**2 } }{ 2 } = 10.271 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 18**2+2 * 7**2 - 18**2 } }{ 2 } = 10.271 ; ;
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