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 = 82.05550904813   b = 10   c = 81.44334642797

Area: T = 407.2177321399
Perimeter: p = 173.4998554761
Semiperimeter: s = 86.74992773805

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 7° = 0.12221730476 rad
Angle ∠ C = γ = 83° = 1.44986232792 rad

Height: ha = 9.92554615164
Height: hb = 81.44334642797
Height: hc = 10

Median: ma = 41.02875452406
Median: mb = 81.59768006351
Median: mc = 41.93216046494

Inradius: r = 4.69441868992
Circumradius: R = 41.02875452406

Vertex coordinates: A[81.44334642797; 0] B[0; 0] C[81.44334642797; 10]
Centroid: CG[54.29656428532; 3.33333333333]
Coordinates of the circumscribed circle: U[40.72217321399; 5]
Coordinates of the inscribed circle: I[76.74992773805; 4.69441868992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 173° = 0.12221730476 rad
∠ C' = γ' = 97° = 1.44986232792 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 = 7° ; ;

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

 alpha + beta + gamma = 180° ; ; gamma = 180° - alpha - beta = 180° - 90 ° - 7 ° = 83 ° ; ;

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 7° } = 82.06 ; ;

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+82.06**2 - 2 * 10 * 82.06 * cos 83° } ; ; c = 81.44 ; ;


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 = 82.06 ; ; b = 10 ; ; c = 81.44 ; ;

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

p = a+b+c = 82.06+10+81.44 = 173.5 ; ;

6. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 173.5 }{ 2 } = 86.75 ; ;

7. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 86.75 * (86.75-82.06)(86.75-10)(86.75-81.44) } ; ; T = sqrt{ 165825.95 } = 407.22 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 407.22 }{ 82.06 } = 9.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 407.22 }{ 10 } = 81.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 407.22 }{ 81.44 } = 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+81.44**2-82.06**2 }{ 2 * 10 * 81.44 } ) = 90° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 82.06**2+81.44**2-10**2 }{ 2 * 82.06 * 81.44 } ) = 7° ; ; gamma = 180° - alpha - beta = 180° - 90° - 7° = 83° ; ;

10. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 407.22 }{ 86.75 } = 4.69 ; ;

11. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 82.06 }{ 2 * sin 90° } = 41.03 ; ;

12. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 81.44**2 - 82.06**2 } }{ 2 } = 41.028 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 81.44**2+2 * 82.06**2 - 10**2 } }{ 2 } = 81.597 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 10**2+2 * 82.06**2 - 81.44**2 } }{ 2 } = 41.932 ; ;
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.