Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, angle β and angle γ.

Obtuse scalene triangle.

Sides: a = 0.03   b = 0.0133445871   c = 0.02327119721

Area: T = 00.0001439774
Perimeter: p = 0.0666157843
Semiperimeter: s = 0.03330789215

Angle ∠ A = α = 109.45° = 109°27' = 1.91102628663 rad
Angle ∠ B = β = 25° = 0.4366332313 rad
Angle ∠ C = γ = 45.55° = 45°33' = 0.79549974743 rad

Height: ha = 0.01095984942
Height: hb = 0.02114158551
Height: hc = 0.01326785479

Median: ma = 0.01111046189
Median: mb = 0.02657433288
Median: mc = 0.02202839174

Inradius: r = 0.00443525425
Circumradius: R = 0.01659078206

Vertex coordinates: A[0.02327119721; 0] B[0; 0] C[0.02771892336; 0.01326785479]
Centroid: CG[0.01766337352; 0.00442261826]
Coordinates of the circumscribed circle: U[0.0111355986; 0.01111400331]
Coordinates of the inscribed circle: I[0.02196330505; 0.00443525425]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 70.55° = 70°33' = 1.91102628663 rad
∠ B' = β' = 155° = 0.4366332313 rad
∠ C' = γ' = 134.45° = 134°27' = 0.79549974743 rad

Calculate another triangle




How did we calculate this triangle?

1. Input data entered: side a, angle β and angle γ.

a = 0.03 ; ; beta = 25° ; ; gamma = 45.55° ; ;

2. From angle β and angle γ we calculate angle α:

 beta + gamma + alpha = 180° ; ; alpha = 180° - beta - gamma = 180° - 25 ° - 45.55 ° = 109.45 ° ; ;

3. From angle β, angle α and side a we calculate b - By using the law of sines, we calculate unknown side b:

 fraction{ b }{ a } = fraction{ sin beta }{ sin alpha } ; ; ; ; b = a * fraction{ sin beta }{ sin alpha } ; ; ; ; b = 0.03 * fraction{ sin 25° }{ sin 109° 27' } = 0.01 ; ;

4. From angle γ, angle α and side a we calculate c - By using the law of sines, we calculate unknown side c:

 fraction{ c }{ a } = fraction{ sin gamma }{ sin alpha } ; ; ; ; c = a * fraction{ sin gamma }{ sin alpha } ; ; ; ; c = 0.03 * fraction{ sin 45° 33' }{ sin 109° 27' } = 0.02 ; ;


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 = 0.03 ; ; b = 0.01 ; ; c = 0.02 ; ;

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

p = a+b+c = 0.03+0.01+0.02 = 0.07 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.07 }{ 2 } = 0.03 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.03 * (0.03-0.03)(0.03-0.01)(0.03-0.02) } ; ; T = sqrt{ 0 } = 0 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.03 } = 0.01 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.01 } = 0.02 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.02 } = 0.01 ; ;

9. 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{ 0.01**2+0.02**2-0.03**2 }{ 2 * 0.01 * 0.02 } ) = 109° 27' ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.03**2+0.02**2-0.01**2 }{ 2 * 0.03 * 0.02 } ) = 25° ; ; gamma = 180° - alpha - beta = 180° - 109° 27' - 25° = 45° 33' ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.03 } = 0 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.03 }{ 2 * sin 109° 27' } = 0.02 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.01**2+2 * 0.02**2 - 0.03**2 } }{ 2 } = 0.011 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.02**2+2 * 0.03**2 - 0.01**2 } }{ 2 } = 0.026 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.01**2+2 * 0.03**2 - 0.02**2 } }{ 2 } = 0.02 ; ;
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.