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 angle γ.

Acute isosceles triangle.

Sides: a = 9.35880020351   b = 9.35880020351   c = 3.25

Area: T = 14.97657285549
Perimeter: p = 21.96660040702
Semiperimeter: s = 10.98330020351

Angle ∠ A = α = 80° = 1.39662634016 rad
Angle ∠ B = β = 80° = 1.39662634016 rad
Angle ∠ C = γ = 20° = 0.34990658504 rad

Height: ha = 3.20106251973
Height: hb = 3.20106251973
Height: hc = 9.21658329569

Median: ma = 5.2132897517
Median: mb = 5.2132897517
Median: mc = 9.21658329569

Inradius: r = 1.36435369007
Circumradius: R = 4.75111821503

Vertex coordinates: A[3.25; 0] B[0; 0] C[1.625; 9.21658329569]
Centroid: CG[1.625; 3.0721944319]
Coordinates of the circumscribed circle: U[1.625; 4.46546508066]
Coordinates of the inscribed circle: I[1.625; 1.36435369007]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 100° = 1.39662634016 rad
∠ B' = β' = 100° = 1.39662634016 rad
∠ C' = γ' = 160° = 0.34990658504 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 = 9.36 ; ; b = 9.36 ; ; c = 3.25 ; ;

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

p = a+b+c = 9.36+9.36+3.25 = 21.97 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 21.97 }{ 2 } = 10.98 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 10.98 * (10.98-9.36)(10.98-9.36)(10.98-3.25) } ; ; T = sqrt{ 224.27 } = 14.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 14.98 }{ 9.36 } = 3.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 14.98 }{ 9.36 } = 3.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 14.98 }{ 3.25 } = 9.22 ; ;

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{ 9.36**2-9.36**2-3.25**2 }{ 2 * 9.36 * 3.25 } ) = 80° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.36**2-9.36**2-3.25**2 }{ 2 * 9.36 * 3.25 } ) = 80° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.25**2-9.36**2-9.36**2 }{ 2 * 9.36 * 9.36 } ) = 20° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 14.98 }{ 10.98 } = 1.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.36 }{ 2 * sin 80° } = 4.75 ; ;




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