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 = 36   b = 52.5   c = 76

Area: T = 841.0221920698
Perimeter: p = 164.5
Semiperimeter: s = 82.25

Angle ∠ A = α = 24.93334239167° = 24°56' = 0.43551703411 rad
Angle ∠ B = β = 37.93660894134° = 37°56'10″ = 0.66221096656 rad
Angle ∠ C = γ = 117.133048667° = 117°7'50″ = 2.04443126469 rad

Height: ha = 46.72334400388
Height: hb = 32.03989303123
Height: hc = 22.13221558078

Median: ma = 62.78663440566
Median: mb = 53.35767006101
Median: mc = 24.12772667329

Inradius: r = 10.22551905252
Circumradius: R = 42.69880547311

Vertex coordinates: A[76; 0] B[0; 0] C[28.39330921053; 22.13221558078]
Centroid: CG[34.79876973684; 7.37773852693]
Coordinates of the circumscribed circle: U[38; -19.47111036621]
Coordinates of the inscribed circle: I[29.75; 10.22551905252]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.0676576083° = 155°4' = 0.43551703411 rad
∠ B' = β' = 142.0643910587° = 142°3'50″ = 0.66221096656 rad
∠ C' = γ' = 62.87695133301° = 62°52'10″ = 2.04443126469 rad

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How did we calculate this triangle?

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

a = 36 ; ; b = 52.5 ; ; c = 76 ; ;

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

p = a+b+c = 36+52.5+76 = 164.5 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 164.5 }{ 2 } = 82.25 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 82.25 * (82.25-36)(82.25-52.5)(82.25-76) } ; ; T = sqrt{ 707317.87 } = 841.02 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 841.02 }{ 36 } = 46.72 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 841.02 }{ 52.5 } = 32.04 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 841.02 }{ 76 } = 22.13 ; ;

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{ 52.5**2+76**2-36**2 }{ 2 * 52.5 * 76 } ) = 24° 56' ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 36**2+76**2-52.5**2 }{ 2 * 36 * 76 } ) = 37° 56'10" ; ; gamma = 180° - alpha - beta = 180° - 24° 56' - 37° 56'10" = 117° 7'50" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 841.02 }{ 82.25 } = 10.23 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 36 }{ 2 * sin 24° 56' } = 42.7 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 52.5**2+2 * 76**2 - 36**2 } }{ 2 } = 62.786 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 76**2+2 * 36**2 - 52.5**2 } }{ 2 } = 53.357 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 52.5**2+2 * 36**2 - 76**2 } }{ 2 } = 24.127 ; ;
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