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.

Acute isosceles triangle.

Sides: a = 20.49656245331   b = 20.49656245331   c = 5.65

Area: T = 57.34775
Perimeter: p = 46.64112490661
Semiperimeter: s = 23.32106245331

Angle ∠ A = α = 82.07774543315° = 82°4'39″ = 1.43325218197 rad
Angle ∠ B = β = 82.07774543315° = 82°4'39″ = 1.43325218197 rad
Angle ∠ C = γ = 15.84550913371° = 15°50'42″ = 0.27765490141 rad

Height: ha = 5.596607246
Height: hb = 5.596607246
Height: hc = 20.3

Median: ma = 10.99990411514
Median: mb = 10.99990411514
Median: mc = 20.3

Inradius: r = 2.45990893747
Circumradius: R = 10.34765671182

Vertex coordinates: A[5.65; 0] B[0; 0] C[2.825; 20.3]
Centroid: CG[2.825; 6.76766666667]
Coordinates of the circumscribed circle: U[2.825; 9.95334328818]
Coordinates of the inscribed circle: I[2.825; 2.45990893747]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 97.92325456685° = 97°55'21″ = 1.43325218197 rad
∠ B' = β' = 97.92325456685° = 97°55'21″ = 1.43325218197 rad
∠ C' = γ' = 164.1554908663° = 164°9'18″ = 0.27765490141 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 = 20.5 ; ; b = 20.5 ; ; c = 5.65 ; ;

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

p = a+b+c = 20.5+20.5+5.65 = 46.64 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 46.64 }{ 2 } = 23.32 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 23.32 * (23.32-20.5)(23.32-20.5)(23.32-5.65) } ; ; T = sqrt{ 3288.74 } = 57.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 57.35 }{ 20.5 } = 5.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 57.35 }{ 20.5 } = 5.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 57.35 }{ 5.65 } = 20.3 ; ;

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{ 20.5**2-20.5**2-5.65**2 }{ 2 * 20.5 * 5.65 } ) = 82° 4'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20.5**2-20.5**2-5.65**2 }{ 2 * 20.5 * 5.65 } ) = 82° 4'39" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 5.65**2-20.5**2-20.5**2 }{ 2 * 20.5 * 20.5 } ) = 15° 50'42" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 57.35 }{ 23.32 } = 2.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20.5 }{ 2 * sin 82° 4'39" } = 10.35 ; ;




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