Isosceles triangle calculator (a)

Please enter two properties of the isosceles triangle

Use symbols: a, b, h, T, p, A, B, C, r, R


You have entered side a and perimeter p.

Acute isosceles triangle.

Sides: a = 94   b = 94   c = 122

Area: T = 4362.673291921
Perimeter: p = 310
Semiperimeter: s = 155

Angle ∠ A = α = 49.53985583927° = 49°32'19″ = 0.86546109506 rad
Angle ∠ B = β = 49.53985583927° = 49°32'19″ = 0.86546109506 rad
Angle ∠ C = γ = 80.92328832147° = 80°55'22″ = 1.41223707523 rad

Height: ha = 92.82328280683
Height: hb = 92.82328280683
Height: hc = 71.51992281838

Median: ma = 98.24395032561
Median: mb = 98.24395032561
Median: mc = 71.51992281838

Inradius: r = 28.14662768981
Circumradius: R = 61.77435972856

Vertex coordinates: A[122; 0] B[0; 0] C[61; 71.51992281838]
Centroid: CG[61; 23.84397427279]
Coordinates of the circumscribed circle: U[61; 9.74656308982]
Coordinates of the inscribed circle: I[61; 28.14662768981]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.4611441607° = 130°27'41″ = 0.86546109506 rad
∠ B' = β' = 130.4611441607° = 130°27'41″ = 0.86546109506 rad
∠ C' = γ' = 99.07771167853° = 99°4'38″ = 1.41223707523 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 = 94 ; ; b = 94 ; ; c = 122 ; ;

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

p = a+b+c = 94+94+122 = 310 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 310 }{ 2 } = 155 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 155 * (155-94)(155-94)(155-122) } ; ; T = sqrt{ 19032915 } = 4362.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4362.67 }{ 94 } = 92.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4362.67 }{ 94 } = 92.82 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4362.67 }{ 122 } = 71.52 ; ;

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{ 94**2-94**2-122**2 }{ 2 * 94 * 122 } ) = 49° 32'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 94**2-94**2-122**2 }{ 2 * 94 * 122 } ) = 49° 32'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 122**2-94**2-94**2 }{ 2 * 94 * 94 } ) = 80° 55'22" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4362.67 }{ 155 } = 28.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 94 }{ 2 * sin 49° 32'19" } = 61.77 ; ;




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