7 30 30 triangle

Acute isosceles triangle.

Sides: a = 7   b = 30   c = 30

Area: T = 104.2832968408
Perimeter: p = 67
Semiperimeter: s = 33.5

Angle ∠ A = α = 13.43995303555° = 13°23'58″ = 0.23438659229 rad
Angle ∠ B = β = 83.33002348222° = 83°18'1″ = 1.45438633653 rad
Angle ∠ C = γ = 83.33002348222° = 83°18'1″ = 1.45438633653 rad

Height: ha = 29.79551338309
Height: hb = 6.95221978939
Height: hc = 6.95221978939

Median: ma = 29.79551338309
Median: mb = 15.79655689989
Median: mc = 15.79655689989

Inradius: r = 3.11329244301
Circumradius: R = 15.10331373967

Vertex coordinates: A[30; 0] B[0; 0] C[0.81766666667; 6.95221978939]
Centroid: CG[10.27222222222; 2.3177399298]
Coordinates of the circumscribed circle: U[15; 1.76220326963]
Coordinates of the inscribed circle: I[3.5; 3.11329244301]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.6600469644° = 166°36'2″ = 0.23438659229 rad
∠ B' = β' = 96.76997651778° = 96°41'59″ = 1.45438633653 rad
∠ C' = γ' = 96.76997651778° = 96°41'59″ = 1.45438633653 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 = 7 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 7+30+30 = 67 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 67 }{ 2 } = 33.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 33.5 * (33.5-7)(33.5-30)(33.5-30) } ; ; T = sqrt{ 10874.94 } = 104.28 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.28 }{ 7 } = 29.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.28 }{ 30 } = 6.95 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.28 }{ 30 } = 6.95 ; ;

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{ 30**2+30**2-7**2 }{ 2 * 30 * 30 } ) = 13° 23'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7**2+30**2-30**2 }{ 2 * 7 * 30 } ) = 83° 18'1" ; ; gamma = 180° - alpha - beta = 180° - 13° 23'58" - 83° 18'1" = 83° 18'1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.28 }{ 33.5 } = 3.11 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7 }{ 2 * sin 13° 23'58" } = 15.1 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 30**2 - 7**2 } }{ 2 } = 29.795 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 7**2 - 30**2 } }{ 2 } = 15.796 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 30**2+2 * 7**2 - 30**2 } }{ 2 } = 15.796 ; ;
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