0.7 1.1 1.7 triangle

Obtuse scalene triangle.

Sides: a = 0.7   b = 1.1   c = 1.7

Area: T = 0.24443742008
Perimeter: p = 3.5
Semiperimeter: s = 1.75

Angle ∠ A = α = 15.15109401512° = 15°9'3″ = 0.26444337904 rad
Angle ∠ B = β = 24.25496286025° = 24°14'59″ = 0.42332358615 rad
Angle ∠ C = γ = 140.5999431246° = 140°35'58″ = 2.45439230017 rad

Height: ha = 0.69882120022
Height: hb = 0.44443167287
Height: hc = 0.28774990597

Median: ma = 1.38883443377
Median: mb = 1.17879218989
Median: mc = 0.35770714214

Inradius: r = 0.14396424004
Circumradius: R = 1.33991348145

Vertex coordinates: A[1.7; 0] B[0; 0] C[0.63882352941; 0.28774990597]
Centroid: CG[0.77994117647; 0.09658330199]
Coordinates of the circumscribed circle: U[0.85; -1.0354785993]
Coordinates of the inscribed circle: I[0.65; 0.14396424004]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.8499059849° = 164°50'57″ = 0.26444337904 rad
∠ B' = β' = 155.7550371397° = 155°45'1″ = 0.42332358615 rad
∠ C' = γ' = 39.40105687537° = 39°24'2″ = 2.45439230017 rad

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How did we calculate this triangle?

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

p = a+b+c = 0.7+1.1+1.7 = 3.5 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 3.5 }{ 2 } = 1.75 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1.75 * (1.75-0.7)(1.75-1.1)(1.75-1.7) } ; ; T = sqrt{ 0.06 } = 0.24 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0.24 }{ 0.7 } = 0.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0.24 }{ 1.1 } = 0.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0.24 }{ 1.7 } = 0.29 ; ;

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{ 1.1**2+1.7**2-0.7**2 }{ 2 * 1.1 * 1.7 } ) = 15° 9'3" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 0.7**2+1.7**2-1.1**2 }{ 2 * 0.7 * 1.7 } ) = 24° 14'59" ; ; gamma = 180° - alpha - beta = 180° - 15° 9'3" - 24° 14'59" = 140° 35'58" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0.24 }{ 1.75 } = 0.14 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 0.7 }{ 2 * sin 15° 9'3" } = 1.34 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.1**2+2 * 1.7**2 - 0.7**2 } }{ 2 } = 1.388 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.7**2+2 * 0.7**2 - 1.1**2 } }{ 2 } = 1.178 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 1.1**2+2 * 0.7**2 - 1.7**2 } }{ 2 } = 0.357 ; ;
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