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.

Obtuse scalene triangle.

Sides: a = 51.08105330788   b = 51.08105330788   c = 96

Area: T = 838.5877419749
Perimeter: p = 198.1611066158
Semiperimeter: s = 99.08105330788

Angle ∠ A = α = 20° = 0.34990658504 rad
Angle ∠ B = β = 20° = 0.34990658504 rad
Angle ∠ C = γ = 140° = 2.44334609528 rad

Height: ha = 32.83439337593
Height: hb = 32.83439337593
Height: hc = 17.47105712448

Median: ma = 72.52879616073
Median: mb = 72.52879616073
Median: mc = 17.47105712448

Inradius: r = 8.4643695074
Circumradius: R = 74.67547436893

Vertex coordinates: A[96; 0] B[0; 0] C[48; 17.47105712448]
Centroid: CG[48; 5.82435237483]
Coordinates of the circumscribed circle: U[48; -57.20441724445]
Coordinates of the inscribed circle: I[48; 8.4643695074]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160° = 0.34990658504 rad
∠ B' = β' = 160° = 0.34990658504 rad
∠ C' = γ' = 40° = 2.44334609528 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 = 51.08 ; ; b = 51.08 ; ; c = 96 ; ;

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

p = a+b+c = 51.08+51.08+96 = 198.16 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 198.16 }{ 2 } = 99.08 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 99.08 * (99.08-51.08)(99.08-51.08)(99.08-96) } ; ; T = sqrt{ 703228.86 } = 838.59 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 838.59 }{ 51.08 } = 32.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 838.59 }{ 51.08 } = 32.83 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 838.59 }{ 96 } = 17.47 ; ;

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{ 51.08**2-51.08**2-96**2 }{ 2 * 51.08 * 96 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 51.08**2-51.08**2-96**2 }{ 2 * 51.08 * 96 } ) = 20° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 96**2-51.08**2-51.08**2 }{ 2 * 51.08 * 51.08 } ) = 140° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 838.59 }{ 99.08 } = 8.46 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 51.08 }{ 2 * sin 20° } = 74.67 ; ;




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