1.5 1.5 0.78 triangle

Acute isosceles triangle.

Sides: a = 1.5   b = 1.5   c = 0.78

Area: T = 0.56548810406
Perimeter: p = 3.78
Semiperimeter: s = 1.89

Angle ∠ A = α = 74.93299378551° = 74°55'48″ = 1.30877741239 rad
Angle ∠ B = β = 74.93299378551° = 74°55'48″ = 1.30877741239 rad
Angle ∠ C = γ = 30.14401242898° = 30°8'24″ = 0.52660444058 rad

Height: ha = 0.75331747208
Height: hb = 0.75331747208
Height: hc = 1.44884129245

Median: ma = 0.9310967239
Median: mb = 0.9310967239
Median: mc = 1.44884129245

Inradius: r = 0.29988788574
Circumradius: R = 0.77767122075

Vertex coordinates: A[0.78; 0] B[0; 0] C[0.39; 1.44884129245]
Centroid: CG[0.39; 0.48328043082]
Coordinates of the circumscribed circle: U[0.39; 0.6721700717]
Coordinates of the inscribed circle: I[0.39; 0.29988788574]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.0770062145° = 105°4'12″ = 1.30877741239 rad
∠ B' = β' = 105.0770062145° = 105°4'12″ = 1.30877741239 rad
∠ C' = γ' = 149.865987571° = 149°51'36″ = 0.52660444058 rad

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How did we calculate this triangle?

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 = 1.5 ; ; b = 1.5 ; ; c = 0.78 ; ;

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

p = a+b+c = 1.5+1.5+0.78 = 3.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.78 }{ 2 } = 1.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.89 * (1.89-1.5)(1.89-1.5)(1.89-0.78) } ; ; T = sqrt{ 0.32 } = 0.56 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.56 }{ 1.5 } = 0.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.56 }{ 1.5 } = 0.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.56 }{ 0.78 } = 1.45 ; ;

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{ 1.5**2+0.78**2-1.5**2 }{ 2 * 1.5 * 0.78 } ) = 74° 55'48" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.5**2+0.78**2-1.5**2 }{ 2 * 1.5 * 0.78 } ) = 74° 55'48" ; ;
 gamma = 180° - alpha - beta = 180° - 74° 55'48" - 74° 55'48" = 30° 8'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.56 }{ 1.89 } = 0.3 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.5 }{ 2 * sin 74° 55'48" } = 0.78 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.5**2+2 * 0.78**2 - 1.5**2 } }{ 2 } = 0.931 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.78**2+2 * 1.5**2 - 1.5**2 } }{ 2 } = 0.931 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.5**2+2 * 1.5**2 - 0.78**2 } }{ 2 } = 1.448 ; ;
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