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 = 20.98877826764   b = 20.98877826764   c = 0.4

Area: T = 4.19773659439
Perimeter: p = 42.37655653528
Semiperimeter: s = 21.18877826764

Angle ∠ A = α = 89.454° = 89°27'14″ = 1.56112668291 rad
Angle ∠ B = β = 89.454° = 89°27'14″ = 1.56112668291 rad
Angle ∠ C = γ = 1.092° = 1°5'31″ = 0.01990589954 rad

Height: ha = 0.43999818379
Height: hb = 0.43999818379
Height: hc = 20.98768297194

Median: ma = 10.49877023876
Median: mb = 10.49877023876
Median: mc = 20.98768297194

Inradius: r = 0.19881031242
Circumradius: R = 10.49443678383

Vertex coordinates: A[0.4; 0] B[0; 0] C[0.2; 20.98768297194]
Centroid: CG[0.2; 6.99656099065]
Coordinates of the circumscribed circle: U[0.2; 10.49224618811]
Coordinates of the inscribed circle: I[0.2; 0.19881031242]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90.546° = 90°32'46″ = 1.56112668291 rad
∠ B' = β' = 90.546° = 90°32'46″ = 1.56112668291 rad
∠ C' = γ' = 178.908° = 178°54'29″ = 0.01990589954 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 = 20.99 ; ; b = 20.99 ; ; c = 0.4 ; ;

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

p = a+b+c = 20.99+20.99+0.4 = 42.38 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 42.38 }{ 2 } = 21.19 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 21.19 * (21.19-20.99)(21.19-20.99)(21.19-0.4) } ; ; T = sqrt{ 17.62 } = 4.2 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.2 }{ 20.99 } = 0.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.2 }{ 20.99 } = 0.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.2 }{ 0.4 } = 20.99 ; ;

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{ 20.99**2-20.99**2-0.4**2 }{ 2 * 20.99 * 0.4 } ) = 89° 27'14" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20.99**2-20.99**2-0.4**2 }{ 2 * 20.99 * 0.4 } ) = 89° 27'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.4**2-20.99**2-20.99**2 }{ 2 * 20.99 * 20.99 } ) = 1° 5'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.2 }{ 21.19 } = 0.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20.99 }{ 2 * sin 89° 27'14" } = 10.49 ; ;




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