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 a and b.

Acute isosceles triangle.

Sides: a = 60.727   b = 60.727   c = 45.545

Area: T = 1281.989896075
Perimeter: p = 166.999
Semiperimeter: s = 83.54995

Angle ∠ A = α = 67.97658143841° = 67°58'33″ = 1.18664017727 rad
Angle ∠ B = β = 67.97658143841° = 67°58'33″ = 1.18664017727 rad
Angle ∠ C = γ = 44.04883712318° = 44°2'54″ = 0.76987891081 rad

Height: ha = 42.22113829353
Height: hb = 42.22113829353
Height: hc = 56.29554862556

Median: ma = 44.2621898341
Median: mb = 44.2621898341
Median: mc = 56.29554862556

Inradius: r = 15.35332531423
Circumradius: R = 32.75436786187

Vertex coordinates: A[45.545; 0] B[0; 0] C[22.77325; 56.29554862556]
Centroid: CG[22.77325; 18.76551620852]
Coordinates of the circumscribed circle: U[22.77325; 23.54218076368]
Coordinates of the inscribed circle: I[22.77325; 15.35332531423]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 112.0244185616° = 112°1'27″ = 1.18664017727 rad
∠ B' = β' = 112.0244185616° = 112°1'27″ = 1.18664017727 rad
∠ C' = γ' = 135.9521628768° = 135°57'6″ = 0.76987891081 rad

Calculate another triangle




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 = 60.73 ; ; b = 60.73 ; ; c = 45.55 ; ;

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

p = a+b+c = 60.73+60.73+45.55 = 167 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 167 }{ 2 } = 83.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 83.5 * (83.5-60.73)(83.5-60.73)(83.5-45.55) } ; ; T = sqrt{ 1643495.7 } = 1281.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1281.99 }{ 60.73 } = 42.22 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1281.99 }{ 60.73 } = 42.22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1281.99 }{ 45.55 } = 56.3 ; ;

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{ 60.73**2-60.73**2-45.55**2 }{ 2 * 60.73 * 45.55 } ) = 67° 58'33" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60.73**2-60.73**2-45.55**2 }{ 2 * 60.73 * 45.55 } ) = 67° 58'33" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 45.55**2-60.73**2-60.73**2 }{ 2 * 60.73 * 60.73 } ) = 44° 2'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1281.99 }{ 83.5 } = 15.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 60.73 }{ 2 * sin 67° 58'33" } = 32.75 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.