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 isosceles triangle.

Sides: a = 106.4187777248   b = 106.4187777248   c = 200

Area: T = 3639.702234266
Perimeter: p = 412.8365554495
Semiperimeter: s = 206.4187777248

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

Height: ha = 68.40440286651
Height: hb = 68.40440286651
Height: hc = 36.39770234266

Median: ma = 151.1099920015
Median: mb = 151.1099920015
Median: mc = 36.39770234266

Inradius: r = 17.63326980708
Circumradius: R = 155.5722382686

Vertex coordinates: A[200; 0] B[0; 0] C[100; 36.39770234266]
Centroid: CG[100; 12.13223411422]
Coordinates of the circumscribed circle: U[100; -119.1755359259]
Coordinates of the inscribed circle: I[100; 17.63326980708]

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 = 106.42 ; ; b = 106.42 ; ; c = 200 ; ;

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

p = a+b+c = 106.42+106.42+200 = 412.84 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 412.84 }{ 2 } = 206.42 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 206.42 * (206.42-106.42)(206.42-106.42)(206.42-200) } ; ; T = sqrt{ 13247433.14 } = 3639.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3639.7 }{ 106.42 } = 68.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3639.7 }{ 106.42 } = 68.4 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3639.7 }{ 200 } = 36.4 ; ;

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{ 106.42**2-106.42**2-200**2 }{ 2 * 106.42 * 200 } ) = 20° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 106.42**2-106.42**2-200**2 }{ 2 * 106.42 * 200 } ) = 20° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 200**2-106.42**2-106.42**2 }{ 2 * 106.42 * 106.42 } ) = 140° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3639.7 }{ 206.42 } = 17.63 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 106.42 }{ 2 * sin 20° } = 155.57 ; ;




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