Isosceles triangle calculator (b,h)

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 height hc.

Acute isosceles triangle.

Sides: a = 4.07770700264   b = 4.07770700264   c = 4.5

Area: T = 7.65
Perimeter: p = 12.65441400528
Semiperimeter: s = 6.32770700264

Angle ∠ A = α = 56.50548153263° = 56°30'17″ = 0.98661950707 rad
Angle ∠ B = β = 56.50548153263° = 56°30'17″ = 0.98661950707 rad
Angle ∠ C = γ = 66.99903693475° = 66°59'25″ = 1.16992025122 rad

Height: ha = 3.75326949258
Height: hb = 3.75326949258
Height: hc = 3.4

Median: ma = 3.77989714209
Median: mb = 3.77989714209
Median: mc = 3.4

Inradius: r = 1.20990904586
Circumradius: R = 2.44444852941

Vertex coordinates: A[4.5; 0] B[0; 0] C[2.25; 3.4]
Centroid: CG[2.25; 1.13333333333]
Coordinates of the circumscribed circle: U[2.25; 0.95655147059]
Coordinates of the inscribed circle: I[2.25; 1.20990904586]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 123.4955184674° = 123°29'43″ = 0.98661950707 rad
∠ B' = β' = 123.4955184674° = 123°29'43″ = 0.98661950707 rad
∠ C' = γ' = 113.0109630653° = 113°35″ = 1.16992025122 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 = 4.08 ; ; b = 4.08 ; ; c = 4.5 ; ;

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

p = a+b+c = 4.08+4.08+4.5 = 12.65 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 12.65 }{ 2 } = 6.33 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 6.33 * (6.33-4.08)(6.33-4.08)(6.33-4.5) } ; ; T = sqrt{ 58.52 } = 7.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.65 }{ 4.08 } = 3.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.65 }{ 4.08 } = 3.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.65 }{ 4.5 } = 3.4 ; ;

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{ 4.08**2-4.08**2-4.5**2 }{ 2 * 4.08 * 4.5 } ) = 56° 30'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.08**2-4.08**2-4.5**2 }{ 2 * 4.08 * 4.5 } ) = 56° 30'17" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 4.5**2-4.08**2-4.08**2 }{ 2 * 4.08 * 4.08 } ) = 66° 59'25" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.65 }{ 6.33 } = 1.21 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.08 }{ 2 * sin 56° 30'17" } = 2.44 ; ;




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

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