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 side b and height hc.

Obtuse isosceles triangle.

Sides: a = 246.2211445045   b = 246.2211445045   c = 450

Area: T = 22500
Perimeter: p = 942.443289009
Semiperimeter: s = 471.2211445045

Angle ∠ A = α = 23.96224889746° = 23°57'45″ = 0.41882243296 rad
Angle ∠ B = β = 23.96224889746° = 23°57'45″ = 0.41882243296 rad
Angle ∠ C = γ = 132.0755022051° = 132°4'30″ = 2.30551439944 rad

Height: ha = 182.7622309724
Height: hb = 182.7622309724
Height: hc = 100

Median: ma = 341.1843601599
Median: mb = 341.1843601599
Median: mc = 100

Inradius: r = 47.7488251351
Circumradius: R = 303.125

Vertex coordinates: A[450; 0] B[0; 0] C[225; 100]
Centroid: CG[225; 33.33333333333]
Coordinates of the circumscribed circle: U[225; -203.125]
Coordinates of the inscribed circle: I[225; 47.7488251351]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0387511025° = 156°2'15″ = 0.41882243296 rad
∠ B' = β' = 156.0387511025° = 156°2'15″ = 0.41882243296 rad
∠ C' = γ' = 47.92549779492° = 47°55'30″ = 2.30551439944 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 = 246.22 ; ; b = 246.22 ; ; c = 450 ; ;

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

p = a+b+c = 246.22+246.22+450 = 942.44 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 942.44 }{ 2 } = 471.22 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 471.22 * (471.22-246.22)(471.22-246.22)(471.22-450) } ; ; T = sqrt{ 506250000 } = 22500 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 22500 }{ 246.22 } = 182.76 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 22500 }{ 246.22 } = 182.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 22500 }{ 450 } = 100 ; ;

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{ 246.22**2-246.22**2-450**2 }{ 2 * 246.22 * 450 } ) = 23° 57'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 246.22**2-246.22**2-450**2 }{ 2 * 246.22 * 450 } ) = 23° 57'45" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 450**2-246.22**2-246.22**2 }{ 2 * 246.22 * 246.22 } ) = 132° 4'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 22500 }{ 471.22 } = 47.75 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 246.22 }{ 2 * sin 23° 57'45" } = 303.13 ; ;




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