10 30 30 triangle

Acute isosceles triangle.

Sides: a = 10   b = 30   c = 30

Area: T = 147.9021994578
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 19.18881364537° = 19°11'17″ = 0.33548961584 rad
Angle ∠ B = β = 80.40659317731° = 80°24'21″ = 1.40333482476 rad
Angle ∠ C = γ = 80.40659317731° = 80°24'21″ = 1.40333482476 rad

Height: ha = 29.58803989155
Height: hb = 9.86601329718
Height: hc = 9.86601329718

Median: ma = 29.58803989155
Median: mb = 16.58331239518
Median: mc = 16.58331239518

Inradius: r = 4.22657712736
Circumradius: R = 15.21327765851

Vertex coordinates: A[30; 0] B[0; 0] C[1.66766666667; 9.86601329718]
Centroid: CG[10.55655555556; 3.28767109906]
Coordinates of the circumscribed circle: U[15; 2.53554627642]
Coordinates of the inscribed circle: I[5; 4.22657712736]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 160.8121863546° = 160°48'43″ = 0.33548961584 rad
∠ B' = β' = 99.59440682269° = 99°35'39″ = 1.40333482476 rad
∠ C' = γ' = 99.59440682269° = 99°35'39″ = 1.40333482476 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 = 10 ; ; b = 30 ; ; c = 30 ; ;

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

p = a+b+c = 10+30+30 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-10)(35-30)(35-30) } ; ; T = sqrt{ 21875 } = 147.9 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 147.9 }{ 10 } = 29.58 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 147.9 }{ 30 } = 9.86 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 147.9 }{ 30 } = 9.86 ; ;

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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 10**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 19° 11'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-10**2-30**2 }{ 2 * 10 * 30 } ) = 80° 24'21" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-10**2-30**2 }{ 2 * 30 * 10 } ) = 80° 24'21" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 147.9 }{ 35 } = 4.23 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 19° 11'17" } = 15.21 ; ;




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