Isosceles triangle calculator (B,h)

Please enter two properties of the isosceles triangle

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


You have entered height hc and angle β.

Acute isosceles triangle.

Sides: a = 50.47701867634   b = 50.47701867634   c = 31.19222908384

Area: T = 748.6154980121
Perimeter: p = 132.1332664365
Semiperimeter: s = 66.06663321826

Angle ∠ A = α = 72° = 1.25766370614 rad
Angle ∠ B = β = 72° = 1.25766370614 rad
Angle ∠ C = γ = 36° = 0.62883185307 rad

Height: ha = 29.666563146
Height: hb = 29.666563146
Height: hc = 48

Median: ma = 33.51655104669
Median: mb = 33.51655104669
Median: mc = 48

Inradius: r = 11.331126292
Circumradius: R = 26.5343747416

Vertex coordinates: A[31.19222908384; 0] B[0; 0] C[15.59661454192; 48]
Centroid: CG[15.59661454192; 16]
Coordinates of the circumscribed circle: U[15.59661454192; 21.4666252584]
Coordinates of the inscribed circle: I[15.59661454192; 11.331126292]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 108° = 1.25766370614 rad
∠ B' = β' = 108° = 1.25766370614 rad
∠ C' = γ' = 144° = 0.62883185307 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 = 50.47 ; ; b = 50.47 ; ; c = 31.19 ; ;

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

p = a+b+c = 50.47+50.47+31.19 = 132.13 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 132.13 }{ 2 } = 66.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 66.07 * (66.07-50.47)(66.07-50.47)(66.07-31.19) } ; ; T = sqrt{ 560424.39 } = 748.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 748.61 }{ 50.47 } = 29.67 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 748.61 }{ 50.47 } = 29.67 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 748.61 }{ 31.19 } = 48 ; ;

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{ 50.47**2-50.47**2-31.19**2 }{ 2 * 50.47 * 31.19 } ) = 72° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 50.47**2-50.47**2-31.19**2 }{ 2 * 50.47 * 31.19 } ) = 72° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 31.19**2-50.47**2-50.47**2 }{ 2 * 50.47 * 50.47 } ) = 36° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 748.61 }{ 66.07 } = 11.33 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50.47 }{ 2 * sin 72° } = 26.53 ; ;




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