Isosceles triangle calculator (a)

Please enter two properties of the isosceles triangle

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


You have entered side a and angle γ.

Obtuse isosceles triangle.

Sides: a = 5.5   b = 5.5   c = 8.04548907178

Area: T = 15.08881562602
Perimeter: p = 19.04548907178
Semiperimeter: s = 9.52224453589

Angle ∠ A = α = 43° = 0.75504915784 rad
Angle ∠ B = β = 43° = 0.75504915784 rad
Angle ∠ C = γ = 94° = 1.64106094969 rad

Height: ha = 5.48766022764
Height: hb = 5.48766022764
Height: hc = 3.75109909803

Median: ma = 6.31884359877
Median: mb = 6.31884359877
Median: mc = 3.75109909803

Inradius: r = 1.58444833645
Circumradius: R = 4.03222677605

Vertex coordinates: A[8.04548907178; 0] B[0; 0] C[4.02224453589; 3.75109909803]
Centroid: CG[4.02224453589; 1.25503303268]
Coordinates of the circumscribed circle: U[4.02224453589; -0.28112767802]
Coordinates of the inscribed circle: I[4.02224453589; 1.58444833645]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 137° = 0.75504915784 rad
∠ B' = β' = 137° = 0.75504915784 rad
∠ C' = γ' = 86° = 1.64106094969 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 = 5.5 ; ; b = 5.5 ; ; c = 8.04 ; ;

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

p = a+b+c = 5.5+5.5+8.04 = 19.04 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19.04 }{ 2 } = 9.52 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.52 * (9.52-5.5)(9.52-5.5)(9.52-8.04) } ; ; T = sqrt{ 227.65 } = 15.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 15.09 }{ 5.5 } = 5.49 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 15.09 }{ 5.5 } = 5.49 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 15.09 }{ 8.04 } = 3.75 ; ;

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{ 5.5**2-5.5**2-8.04**2 }{ 2 * 5.5 * 8.04 } ) = 43° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 5.5**2-5.5**2-8.04**2 }{ 2 * 5.5 * 8.04 } ) = 43° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.04**2-5.5**2-5.5**2 }{ 2 * 5.5 * 5.5 } ) = 94° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 15.09 }{ 9.52 } = 1.58 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.5 }{ 2 * sin 43° } = 4.03 ; ;




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