1.5 3.6 3.9 triangle

Right scalene triangle.

Sides: a = 1.5   b = 3.6   c = 3.9

Area: T = 2.7
Perimeter: p = 9
Semiperimeter: s = 4.5

Angle ∠ A = α = 22.6219864948° = 22°37'11″ = 0.39547911197 rad
Angle ∠ B = β = 67.3880135052° = 67°22'49″ = 1.17660052071 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 3.6
Height: hb = 1.5
Height: hc = 1.38546153846

Median: ma = 3.67772952016
Median: mb = 2.34330749028
Median: mc = 1.95

Inradius: r = 0.6
Circumradius: R = 1.95

Vertex coordinates: A[3.9; 0] B[0; 0] C[0.57769230769; 1.38546153846]
Centroid: CG[1.49223076923; 0.46215384615]
Coordinates of the circumscribed circle: U[1.95; 0]
Coordinates of the inscribed circle: I[0.9; 0.6]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 157.3880135052° = 157°22'49″ = 0.39547911197 rad
∠ B' = β' = 112.6219864948° = 112°37'11″ = 1.17660052071 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

a = 1.5 ; ; b = 3.6 ; ; c = 3.9 ; ;

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

p = a+b+c = 1.5+3.6+3.9 = 9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 9 }{ 2 } = 4.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 4.5 * (4.5-1.5)(4.5-3.6)(4.5-3.9) } ; ; T = sqrt{ 7.29 } = 2.7 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2.7 }{ 1.5 } = 3.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2.7 }{ 3.6 } = 1.5 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2.7 }{ 3.9 } = 1.38 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 1.5**2-3.6**2-3.9**2 }{ 2 * 3.6 * 3.9 } ) = 22° 37'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 3.6**2-1.5**2-3.9**2 }{ 2 * 1.5 * 3.9 } ) = 67° 22'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 3.9**2-1.5**2-3.6**2 }{ 2 * 3.6 * 1.5 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2.7 }{ 4.5 } = 0.6 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1.5 }{ 2 * sin 22° 37'11" } = 1.95 ; ;

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