35 65 95 triangle

Obtuse scalene triangle.

Sides: a = 35   b = 65   c = 95

Area: T = 703.6465640575
Perimeter: p = 195
Semiperimeter: s = 97.5

Angle ∠ A = α = 13.17435511073° = 13°10'25″ = 0.2329921841 rad
Angle ∠ B = β = 25.04396595945° = 25°2'23″ = 0.43770245035 rad
Angle ∠ C = γ = 141.7876789298° = 141°47'12″ = 2.47546463091 rad

Height: ha = 40.20883223186
Height: hb = 21.65106350946
Height: hc = 14.81435924332

Median: ma = 79.49105654779
Median: mb = 63.78767541109
Median: mc = 21.65106350946

Inradius: r = 7.21768783649
Circumradius: R = 76.78875858022

Vertex coordinates: A[95; 0] B[0; 0] C[31.71105263158; 14.81435924332]
Centroid: CG[42.23768421053; 4.93878641444]
Coordinates of the circumscribed circle: U[47.5; -60.33331031303]
Coordinates of the inscribed circle: I[32.5; 7.21768783649]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.8266448893° = 166°49'35″ = 0.2329921841 rad
∠ B' = β' = 154.9660340406° = 154°57'37″ = 0.43770245035 rad
∠ C' = γ' = 38.21332107017° = 38°12'48″ = 2.47546463091 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 = 35 ; ; b = 65 ; ; c = 95 ; ;

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

p = a+b+c = 35+65+95 = 195 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 195 }{ 2 } = 97.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 97.5 * (97.5-35)(97.5-65)(97.5-95) } ; ; T = sqrt{ 495117.19 } = 703.65 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 703.65 }{ 35 } = 40.21 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 703.65 }{ 65 } = 21.65 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 703.65 }{ 95 } = 14.81 ; ;

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{ 65**2+95**2-35**2 }{ 2 * 65 * 95 } ) = 13° 10'25" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 35**2+95**2-65**2 }{ 2 * 35 * 95 } ) = 25° 2'23" ; ;
 gamma = 180° - alpha - beta = 180° - 13° 10'25" - 25° 2'23" = 141° 47'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 703.65 }{ 97.5 } = 7.22 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 35 }{ 2 * sin 13° 10'25" } = 76.79 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 65**2+2 * 95**2 - 35**2 } }{ 2 } = 79.491 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 95**2+2 * 35**2 - 65**2 } }{ 2 } = 63.787 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 65**2+2 * 35**2 - 95**2 } }{ 2 } = 21.651 ; ;
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