Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 2.1   b = 7.2   c = 7.5

Area: T = 7.56
Perimeter: p = 16.8
Semiperimeter: s = 8.4

Angle ∠ A = α = 16.26602047083° = 16°15'37″ = 0.28437941092 rad
Angle ∠ B = β = 73.74397952917° = 73°44'23″ = 1.28770022176 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 7.2
Height: hb = 2.1
Height: hc = 2.016

Median: ma = 7.27661597014
Median: mb = 4.16877331968
Median: mc = 3.75

Inradius: r = 0.9
Circumradius: R = 3.75

Vertex coordinates: A[7.5; 0] B[0; 0] C[0.588; 2.016]
Centroid: CG[2.696; 0.672]
Coordinates of the circumscribed circle: U[3.75; 0]
Coordinates of the inscribed circle: I[1.2; 0.9]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.7439795292° = 163°44'23″ = 0.28437941092 rad
∠ B' = β' = 106.2660204708° = 106°15'37″ = 1.28770022176 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

a = 2.1 ; ; b = 7.2 ; ; c = 7.5 ; ;

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

p = a+b+c = 2.1+7.2+7.5 = 16.8 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.8 }{ 2 } = 8.4 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.4 * (8.4-2.1)(8.4-7.2)(8.4-7.5) } ; ; T = sqrt{ 57.15 } = 7.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.56 }{ 2.1 } = 7.2 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.56 }{ 7.2 } = 2.1 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.56 }{ 7.5 } = 2.02 ; ;

5. 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{ 7.2**2+7.5**2-2.1**2 }{ 2 * 7.2 * 7.5 } ) = 16° 15'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 2.1**2+7.5**2-7.2**2 }{ 2 * 2.1 * 7.5 } ) = 73° 44'23" ; ; gamma = 180° - alpha - beta = 180° - 16° 15'37" - 73° 44'23" = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.56 }{ 8.4 } = 0.9 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 2.1 }{ 2 * sin 16° 15'37" } = 3.75 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.2**2+2 * 7.5**2 - 2.1**2 } }{ 2 } = 7.276 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.5**2+2 * 2.1**2 - 7.2**2 } }{ 2 } = 4.168 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.2**2+2 * 2.1**2 - 7.5**2 } }{ 2 } = 3.75 ; ;
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