Triangle calculator ASA

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


Right scalene triangle.

Sides: a = 91673351.94108   b = 91673037.78113   c = 240000

Area: T = 1.10007645338E+13
Perimeter: p = 183586389.722
Semiperimeter: s = 91793194.861

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 89.85° = 89°51' = 1.56881783329 rad
Angle ∠ C = γ = 0.15° = 0°9' = 0.00326179939 rad

Height: ha = 239999.1787533
Height: hb = 240000
Height: hc = 91673037.78113

Median: ma = 45836675.97704
Median: mb = 45837147.20663
Median: mc = 91673116.32113

Inradius: r = 119842.9220278
Circumradius: R = 45836675.97704

Vertex coordinates: A[240000; 0] B[0; 0] C[240000; 91673037.78113]
Centroid: CG[160000; 30557679.26604]
Coordinates of the circumscribed circle: U[120000; 45836518.89107]
Coordinates of the inscribed circle: I[120157.0879722; 119842.9220278]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 90.15° = 90°9' = 1.56881783329 rad
∠ C' = γ' = 179.85° = 179°51' = 0.00326179939 rad

Calculate another triangle


How did we calculate this triangle?

1. Calculate the third unknown inner angle

 alpha = 90° ; ; beta = 89° 51' ; ; ; ; alpha + beta + gamma = 180° ; ; ; ; gamma = 180° - alpha - beta = 180° - 90° - 89° 51' = 0° 9' ; ;

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

c = 240000 ; ; ; ; fraction{ a }{ c } = fraction{ sin alpha }{ sin gamma } ; ; ; ; a = c * fraction{ sin alpha }{ sin gamma } ; ; ; ; a = 240000 * fraction{ sin 90° }{ sin 0° 9' } = 91673351.94 ; ;

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 = 240000 * fraction{ sin 89° 51' }{ sin 0° 9' } = 91673037.78 ; ;
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 = 91673351.94 ; ; b = 91673037.78 ; ; c = 240000 ; ;

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

p = a+b+c = 91673351.94+91673037.78+240000 = 183586389.72 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 183586389.72 }{ 2 } = 91793194.86 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 91793194.86 * (91793194.86-91673351.94)(91793194.86-91673037.78)(91793194.86-240000) } ; ; T = sqrt{ 1.21 * 10**{ 26 } } = 1.1 * 10**{ 13 } ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.1 * 10**{ 13 } }{ 91673351.94 } = 239999.18 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.1 * 10**{ 13 } }{ 91673037.78 } = 240000 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.1 * 10**{ 13 } }{ 240000 } = 91673037.78 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 91673037.78**2+240000**2-91673351.94**2 }{ 2 * 91673037.78 * 240000 } ) = 90° ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 91673351.94**2+240000**2-91673037.78**2 }{ 2 * 91673351.94 * 240000 } ) = 89° 51' ; ;
 gamma = 180° - alpha - beta = 180° - 90° - 89° 51' = 0° 9' ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.1 * 10**{ 13 } }{ 91793194.86 } = 119842.92 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 91673351.94 }{ 2 * sin 90° } = 45836675.97 ; ;

11. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 91673037.78**2+2 * 240000**2 - 91673351.94**2 } }{ 2 } = 45836675.97 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 240000**2+2 * 91673351.94**2 - 91673037.78**2 } }{ 2 } = 45837147.206 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 91673037.78**2+2 * 91673351.94**2 - 240000**2 } }{ 2 } = 91673116.321 ; ;
Calculate another triangle


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

See more information about triangles or more details on solving triangles.