Triangle calculator ASA

Please enter the side of the triangle and two adjacent angles
°
°


Right scalene triangle.

Sides: a = 0.04325426705   b = 9.75500928139   c = 9.75

Area: T = 0.20773955187
Perimeter: p = 19.54326354844
Semiperimeter: s = 9.77113177422

Angle ∠ A = α = 0.25° = 0°15' = 0.00443633231 rad
Angle ∠ B = β = 90° = 1.57107963268 rad
Angle ∠ C = γ = 89.75° = 89°45' = 1.56664330037 rad

Height: ha = 9.75
Height: hb = 0.04325422655
Height: hc = 0.04325426705

Median: ma = 9.75500232035
Median: mb = 4.87550464069
Median: mc = 4.87551856251

Inradius: r = 0.02112249283
Circumradius: R = 4.87550464069

Vertex coordinates: A[9.75; 0] B[0; 0] C[-0; 0.04325426705]
Centroid: CG[3.25; 0.01441808902]
Coordinates of the circumscribed circle: U[4.875; 0.02112713353]
Coordinates of the inscribed circle: I[0.02112249283; 0.02112249283]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 179.75° = 179°45' = 0.00443633231 rad
∠ B' = β' = 90° = 1.57107963268 rad
∠ C' = γ' = 90.25° = 90°15' = 1.56664330037 rad

Calculate another triangle




How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 0° 15' ; ; beta = 90° ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 0° 15' - 90° = 89° 45' ; ;

2. By using the law of sines, we calculate unknown side a

c = 9.75 ; ; ; ; fraction{ a }{ c } = fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = c * fraction{ sin( alpha ) }{ sin ( gamma ) } ; ; ; ; a = 9.75 * fraction{ sin(0° 15') }{ sin (89° 45') } = 0.04 ; ;

3. By using the law of sines, we calculate last unknown side b

 fraction{ b }{ c } = fraction{ sin( beta ) }{ sin ( gamma ) } ; ; ; ; b = c * fraction{ sin( beta ) }{ sin ( gamma ) } ; ; ; ; b = 9.75 * fraction{ sin(90° ) }{ sin (89° 45') } = 9.75 ; ;


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 = 0.04 ; ; b = 9.75 ; ; c = 9.75 ; ;

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

p = a+b+c = 0.04+9.75+9.75 = 19.54 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 19.54 }{ 2 } = 9.77 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.77 * (9.77-0.04)(9.77-9.75)(9.77-9.75) } ; ; T = sqrt{ 0.04 } = 0.21 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.21 }{ 0.04 } = 9.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.21 }{ 9.75 } = 0.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.21 }{ 9.75 } = 0.04 ; ;

8. 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{ 0.04**2-9.75**2-9.75**2 }{ 2 * 9.75 * 9.75 } ) = 0° 15' ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 9.75**2-0.04**2-9.75**2 }{ 2 * 0.04 * 9.75 } ) = 90° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.75**2-0.04**2-9.75**2 }{ 2 * 9.75 * 0.04 } ) = 89° 45' ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.21 }{ 9.77 } = 0.02 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.04 }{ 2 * sin 0° 15' } = 4.88 ; ;




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

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