0.07 0.75 0.75 triangle

Acute isosceles triangle.

Sides: a = 0.07   b = 0.75   c = 0.75

Area: T = 0.02662214011
Perimeter: p = 1.57
Semiperimeter: s = 0.785

Angle ∠ A = α = 5.35495489755° = 5°20'58″ = 0.09333672431 rad
Angle ∠ B = β = 87.32552255123° = 87°19'31″ = 1.52441127052 rad
Angle ∠ C = γ = 87.32552255123° = 87°19'31″ = 1.52441127052 rad

Height: ha = 0.74991828882
Height: hb = 0.07699237362
Height: hc = 0.07699237362

Median: ma = 0.74991828882
Median: mb = 0.37882525611
Median: mc = 0.37882525611

Inradius: r = 0.03334030587
Circumradius: R = 0.37554090015

Vertex coordinates: A[0.75; 0] B[0; 0] C[0.00332666667; 0.07699237362]
Centroid: CG[0.25110888889; 0.02333079121]
Coordinates of the circumscribed circle: U[0.375; 0.01875190867]
Coordinates of the inscribed circle: I[0.035; 0.03334030587]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.6550451025° = 174°39'2″ = 0.09333672431 rad
∠ B' = β' = 92.67547744877° = 92°40'29″ = 1.52441127052 rad
∠ C' = γ' = 92.67547744877° = 92°40'29″ = 1.52441127052 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 = 0.07 ; ; b = 0.75 ; ; c = 0.75 ; ;

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

p = a+b+c = 0.07+0.75+0.75 = 1.57 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 1.57 }{ 2 } = 0.79 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.79 * (0.79-0.07)(0.79-0.75)(0.79-0.75) } ; ; T = sqrt{ 0 } = 0.03 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.03 }{ 0.07 } = 0.75 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.03 }{ 0.75 } = 0.07 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.03 }{ 0.75 } = 0.07 ; ;

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{ 0.75**2+0.75**2-0.07**2 }{ 2 * 0.75 * 0.75 } ) = 5° 20'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.07**2+0.75**2-0.75**2 }{ 2 * 0.07 * 0.75 } ) = 87° 19'31" ; ;
 gamma = 180° - alpha - beta = 180° - 5° 20'58" - 87° 19'31" = 87° 19'31" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.03 }{ 0.79 } = 0.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.07 }{ 2 * sin 5° 20'58" } = 0.38 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.75**2+2 * 0.75**2 - 0.07**2 } }{ 2 } = 0.749 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.75**2+2 * 0.07**2 - 0.75**2 } }{ 2 } = 0.378 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 0.75**2+2 * 0.07**2 - 0.75**2 } }{ 2 } = 0.378 ; ;
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