Isosceles triangle calculator (b)

Please enter two properties of the isosceles triangle

Use symbols: a, b, h, T, p, A, B, C, r, R


You have entered side b and perimeter p.

Obtuse isosceles triangle.

Sides: a = 8.6   b = 8.6   c = 15.3

Area: T = 30.0577296847
Perimeter: p = 32.5
Semiperimeter: s = 16.25

Angle ∠ A = α = 27.18551413434° = 27°11'7″ = 0.47444702241 rad
Angle ∠ B = β = 27.18551413434° = 27°11'7″ = 0.47444702241 rad
Angle ∠ C = γ = 125.6329717313° = 125°37'47″ = 2.19326522055 rad

Height: ha = 6.99900690342
Height: hb = 6.99900690342
Height: hc = 3.92990584114

Median: ma = 11.64219500085
Median: mb = 11.64219500085
Median: mc = 3.92990584114

Inradius: r = 1.8549679806
Circumradius: R = 9.41219242139

Vertex coordinates: A[15.3; 0] B[0; 0] C[7.65; 3.92990584114]
Centroid: CG[7.65; 1.31096861371]
Coordinates of the circumscribed circle: U[7.65; -5.48328658026]
Coordinates of the inscribed circle: I[7.65; 1.8549679806]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.8154858657° = 152°48'53″ = 0.47444702241 rad
∠ B' = β' = 152.8154858657° = 152°48'53″ = 0.47444702241 rad
∠ C' = γ' = 54.37702826868° = 54°22'13″ = 2.19326522055 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 = 8.6 ; ; b = 8.6 ; ; c = 15.3 ; ;

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

p = a+b+c = 8.6+8.6+15.3 = 32.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32.5 }{ 2 } = 16.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.25 * (16.25-8.6)(16.25-8.6)(16.25-15.3) } ; ; T = sqrt{ 903.44 } = 30.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 30.06 }{ 8.6 } = 6.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 30.06 }{ 8.6 } = 6.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 30.06 }{ 15.3 } = 3.93 ; ;

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{ 8.6**2-8.6**2-15.3**2 }{ 2 * 8.6 * 15.3 } ) = 27° 11'7" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.6**2-8.6**2-15.3**2 }{ 2 * 8.6 * 15.3 } ) = 27° 11'7" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15.3**2-8.6**2-8.6**2 }{ 2 * 8.6 * 8.6 } ) = 125° 37'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 30.06 }{ 16.25 } = 1.85 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.6 }{ 2 * sin 27° 11'7" } = 9.41 ; ;




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