Isosceles triangle calculator (A,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 α.

Obtuse isosceles triangle.

Sides: a = 8.28113312084   b = 8.28113312084   c = 12.5

Area: T = 33.95765131959
Perimeter: p = 29.06326624169
Semiperimeter: s = 14.53113312084

Angle ∠ A = α = 41° = 0.71655849933 rad
Angle ∠ B = β = 41° = 0.71655849933 rad
Angle ∠ C = γ = 98° = 1.7110422667 rad

Height: ha = 8.20107378624
Height: hb = 8.20107378624
Height: hc = 5.43330421114

Median: ma = 9.76106409444
Median: mb = 9.76106409444
Median: mc = 5.43330421114

Inradius: r = 2.33767792468
Circumradius: R = 6.31114223282

Vertex coordinates: A[12.5; 0] B[0; 0] C[6.25; 5.43330421114]
Centroid: CG[6.25; 1.81110140371]
Coordinates of the circumscribed circle: U[6.25; -0.87883802169]
Coordinates of the inscribed circle: I[6.25; 2.33767792468]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139° = 0.71655849933 rad
∠ B' = β' = 139° = 0.71655849933 rad
∠ C' = γ' = 82° = 1.7110422667 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 = 8.28 ; ; b = 8.28 ; ; c = 12.5 ; ;

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

p = a+b+c = 8.28+8.28+12.5 = 29.06 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 29.06 }{ 2 } = 14.53 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 14.53 * (14.53-8.28)(14.53-8.28)(14.53-12.5) } ; ; T = sqrt{ 1153.04 } = 33.96 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 33.96 }{ 8.28 } = 8.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 33.96 }{ 8.28 } = 8.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 33.96 }{ 12.5 } = 5.43 ; ;

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{ 8.28**2-8.28**2-12.5**2 }{ 2 * 8.28 * 12.5 } ) = 41° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 8.28**2-8.28**2-12.5**2 }{ 2 * 8.28 * 12.5 } ) = 41° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.5**2-8.28**2-8.28**2 }{ 2 * 8.28 * 8.28 } ) = 98° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 33.96 }{ 14.53 } = 2.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8.28 }{ 2 * sin 41° } = 6.31 ; ;




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