Triangle calculator SSS - result

Please enter the triangle sides:


Acute isosceles triangle.

Sides: a = 2.3   b = 2.3   c = 3.25

Area: T = 2.64549963817
Perimeter: p = 7.85
Semiperimeter: s = 3.925

Angle ∠ A = α = 45.04773854725° = 45°2'51″ = 0.78662251959 rad
Angle ∠ B = β = 45.04773854725° = 45°2'51″ = 0.78662251959 rad
Angle ∠ C = γ = 89.90552290549° = 89°54'19″ = 1.56991422618 rad

Height: ha = 2.32999968537
Height: hb = 2.32999968537
Height: hc = 1.62876900811

Median: ma = 2.57697762549
Median: mb = 2.57697762549
Median: mc = 1.62876900811

Inradius: r = 0.67438844285
Circumradius: R = 1.62550022229

Vertex coordinates: A[3.25; 0] B[0; 0] C[1.625; 1.62876900811]
Centroid: CG[1.625; 0.54325633604]
Coordinates of the circumscribed circle: U[1.625; 0.00326878581]
Coordinates of the inscribed circle: I[1.625; 0.67438844285]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.9532614527° = 134°57'9″ = 0.78662251959 rad
∠ B' = β' = 134.9532614527° = 134°57'9″ = 0.78662251959 rad
∠ C' = γ' = 90.09547709451° = 90°5'41″ = 1.56991422618 rad

Calculate another triangle




How did we calculate this triangle?

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

p = a+b+c = 2.3+2.3+3.25 = 7.85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 7.85 }{ 2 } = 3.93 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.93 * (3.93-2.3)(3.93-2.3)(3.93-3.25) } ; ; T = sqrt{ 7 } = 2.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.64 }{ 2.3 } = 2.3 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.64 }{ 2.3 } = 2.3 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.64 }{ 3.25 } = 1.63 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 2.3**2+3.25**2-2.3**2 }{ 2 * 2.3 * 3.25 } ) = 45° 2'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.3**2+3.25**2-2.3**2 }{ 2 * 2.3 * 3.25 } ) = 45° 2'51" ; ; gamma = 180° - alpha - beta = 180° - 45° 2'51" - 45° 2'51" = 89° 54'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.64 }{ 3.93 } = 0.67 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.3 }{ 2 * sin 45° 2'51" } = 1.63 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.3**2+2 * 3.25**2 - 2.3**2 } }{ 2 } = 2.57 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.25**2+2 * 2.3**2 - 2.3**2 } }{ 2 } = 2.57 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.3**2+2 * 2.3**2 - 3.25**2 } }{ 2 } = 1.628 ; ;
Calculate another triangle

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

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