Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 90   b = 55   c = 50

Area: T = 1214.994421295
Perimeter: p = 195
Semiperimeter: s = 97.5

Angle ∠ A = α = 117.9166339005° = 117°54'59″ = 2.05880283575 rad
Angle ∠ B = β = 32.68334637577° = 32°41' = 0.57704340535 rad
Angle ∠ C = γ = 29.44001972368° = 29°24'1″ = 0.51331302425 rad

Height: ha = 276.9998713989
Height: hb = 44.18216077436
Height: hc = 48.6599768518

Median: ma = 27.1576951228
Median: mb = 67.40773438136
Median: mc = 70.26773466128

Inradius: r = 12.46114791072
Circumradius: R = 50.92661684875

Vertex coordinates: A[50; 0] B[0; 0] C[75.75; 48.6599768518]
Centroid: CG[41.91766666667; 16.21999228393]
Coordinates of the circumscribed circle: U[25; 44.36774952732]
Coordinates of the inscribed circle: I[42.5; 12.46114791072]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 62.08436609946° = 62°5'1″ = 2.05880283575 rad
∠ B' = β' = 147.3176536242° = 147°19' = 0.57704340535 rad
∠ C' = γ' = 150.6599802763° = 150°35'59″ = 0.51331302425 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 90 ; ; b = 55 ; ; c = 50 ; ;


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 = 90 ; ; b = 55 ; ; c = 50 ; ; : Nr. 1

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

p = a+b+c = 90+55+50 = 195 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 195 }{ 2 } = 97.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 97.5 * (97.5-90)(97.5-55)(97.5-50) } ; ; T = sqrt{ 1476210.94 } = 1214.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1214.99 }{ 90 } = 27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1214.99 }{ 55 } = 44.18 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1214.99 }{ 50 } = 48.6 ; ;

6. 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{ 55**2+50**2-90**2 }{ 2 * 55 * 50 } ) = 117° 54'59" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 90**2+50**2-55**2 }{ 2 * 90 * 50 } ) = 32° 41' ; ; gamma = 180° - alpha - beta = 180° - 117° 54'59" - 32° 41' = 29° 24'1" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1214.99 }{ 97.5 } = 12.46 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 90 }{ 2 * sin 117° 54'59" } = 50.93 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 50**2 - 90**2 } }{ 2 } = 27.157 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 50**2+2 * 90**2 - 55**2 } }{ 2 } = 67.407 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 55**2+2 * 90**2 - 50**2 } }{ 2 } = 70.267 ; ;
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