Triangle calculator - result

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

You have entered side b, angle α and angle β.

Right scalene triangle.

Sides: a = 26.69546716255   b = 10   c = 24.75108685342

Area: T = 123.7544342671
Perimeter: p = 61.44655401597
Semiperimeter: s = 30.72327700799

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 22° = 0.38439724354 rad
Angle ∠ C = γ = 68° = 1.18768238914 rad

Height: ha = 9.27218385457
Height: hb = 24.75108685342
Height: hc = 10

Median: ma = 13.34773358128
Median: mb = 25.25108513361
Median: mc = 15.91107313879

Inradius: r = 4.02880984543
Circumradius: R = 13.34773358128

Vertex coordinates: A[24.75108685342; 0] B[0; 0] C[24.75108685342; 10]
Centroid: CG[16.50105790228; 3.33333333333]
Coordinates of the circumscribed circle: U[12.37554342671; 5]
Coordinates of the inscribed circle: I[20.72327700799; 4.02880984543]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 158° = 0.38439724354 rad
∠ C' = γ' = 112° = 1.18768238914 rad

Calculate another triangle


How did we calculate this triangle?

1. Input data entered: side b, angle α and angle β.

b = 10 ; ; alpha = 90° ; ; beta = 22° ; ;

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

 alpha + beta + gamma = 180° ; ; gamma = 180° - alpha - beta = 180° - 90 ° - 22 ° = 68 ° ; ;

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

 fraction{ a }{ b } = fraction{ sin alpha }{ sin beta } ; ; ; ; a = b * fraction{ sin alpha }{ sin beta } ; ; ; ; a = 10 * fraction{ sin 90° }{ sin 22° } = 26.69 ; ;

4. Calculation of the third side c of the triangle using a Law of Cosines

c**2 = b**2+a**2 - 2ba cos gamma ; ; c = sqrt{ b**2+a**2 - 2ba cos gamma } ; ; c = sqrt{ 10**2+26.69**2 - 2 * 10 * 26.69 * cos 68° } ; ; c = 24.75 ; ;
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 = 26.69 ; ; b = 10 ; ; c = 24.75 ; ;

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

p = a+b+c = 26.69+10+24.75 = 61.45 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 61.45 }{ 2 } = 30.72 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 30.72 * (30.72-26.69)(30.72-10)(30.72-24.75) } ; ; T = sqrt{ 15315.14 } = 123.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 123.75 }{ 26.69 } = 9.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 123.75 }{ 10 } = 24.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 123.75 }{ 24.75 } = 10 ; ;

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{ 10**2+24.75**2-26.69**2 }{ 2 * 10 * 24.75 } ) = 90° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 26.69**2+24.75**2-10**2 }{ 2 * 26.69 * 24.75 } ) = 22° ; ; gamma = 180° - alpha - beta = 180° - 90° - 22° = 68° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 123.75 }{ 30.72 } = 4.03 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 26.69 }{ 2 * sin 90° } = 13.35 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 24.75**2 - 26.69**2 } }{ 2 } = 13.347 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 24.75**2+2 * 26.69**2 - 10**2 } }{ 2 } = 25.251 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 26.69**2 - 24.75**2 } }{ 2 } = 15.911 ; ;
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.