Triangle calculator

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

You have entered side a, b and c.

Right scalene triangle.

Sides: a = 0.7   b = 2.4   c = 2.5

Area: T = 0.84
Perimeter: p = 5.6
Semiperimeter: s = 2.8

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 = 2.4
Height: hb = 0.7
Height: hc = 0.672

Median: ma = 2.42553865671
Median: mb = 1.38992443989
Median: mc = 1.25

Inradius: r = 0.3
Circumradius: R = 1.25

Vertex coordinates: A[2.5; 0] B[0; 0] C[0.196; 0.672]
Centroid: CG[0.89986666667; 0.224]
Coordinates of the circumscribed circle: U[1.25; -0]
Coordinates of the inscribed circle: I[0.4; 0.3]

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?

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

a = 0.7 ; ; b = 2.4 ; ; c = 2.5 ; ;


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 = 0.7 ; ; b = 2.4 ; ; c = 2.5 ; ; : Nr. 1

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

p = a+b+c = 0.7+2.4+2.5 = 5.6 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 5.6 }{ 2 } = 2.8 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 2.8 * (2.8-0.7)(2.8-2.4)(2.8-2.5) } ; ; T = sqrt{ 0.71 } = 0.84 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.84 }{ 0.7 } = 2.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.84 }{ 2.4 } = 0.7 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.84 }{ 2.5 } = 0.67 ; ;

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{ 2.4**2+2.5**2-0.7**2 }{ 2 * 2.4 * 2.5 } ) = 16° 15'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.7**2+2.5**2-2.4**2 }{ 2 * 0.7 * 2.5 } ) = 73° 44'23" ; ; gamma = 180° - alpha - beta = 180° - 16° 15'37" - 73° 44'23" = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.84 }{ 2.8 } = 0.3 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.7 }{ 2 * sin 16° 15'37" } = 1.25 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.4**2+2 * 2.5**2 - 0.7**2 } }{ 2 } = 2.425 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.5**2+2 * 0.7**2 - 2.4**2 } }{ 2 } = 1.389 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.4**2+2 * 0.7**2 - 2.5**2 } }{ 2 } = 1.25 ; ;
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