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: h_a = 17.6566443583
Height: h_b = 6.86663947267
Height: h_c = 6.86663947267

Median: m_a = 17.6566443583
Median: m_b = 10.27113192921
Median: m_c = 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

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.

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

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

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

6. Inradius

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

7. Circumradius

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

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