24 30 30 triangle

Acute isosceles triangle.

Sides: a = 24 b = 30 c = 30

Area: T = 329.9455450037
Perimeter: p = 84
Semiperimeter: s = 42

Angle ∠ A = α = 47.15663569564° = 47°9'23″ = 0.82330336921 rad
Angle ∠ B = β = 66.42218215218° = 66°25'19″ = 1.15992794807 rad
Angle ∠ C = γ = 66.42218215218° = 66°25'19″ = 1.15992794807 rad

Height: h_a = 27.49554541697
Height: h_b = 21.99663633358
Height: h_c = 21.99663633358

Median: m_a = 27.49554541697
Median: m_b = 22.65495033058
Median: m_c = 22.65495033058

Inradius: r = 7.85658440485
Circumradius: R = 16.36663417677

Vertex coordinates: A[30; 0] B[0; 0] C[9.6; 21.99663633358]
Centroid: CG[13.2; 7.33221211119]
Coordinates of the circumscribed circle: U[15; 6.54765367071]
Coordinates of the inscribed circle: I[12; 7.85658440485]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 132.8443643044° = 132°50'37″ = 0.82330336921 rad
∠ B' = β' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad
∠ C' = γ' = 113.5788178478° = 113°34'41″ = 1.15992794807 rad

Calculate another triangle

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.

$a = 24 ; ; b = 30 ; ; c = 30 ; ;$

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

$p = a+b+c = 24+30+30 = 84 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 84 }{ 2 } = 42 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 42 * (42-24)(42-30)(42-30) } ; ; T = sqrt{ 108864 } = 329.95 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 329.95 }{ 24 } = 27.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 329.95 }{ 30 } = 22 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 329.95 }{ 30 } = 22 ; ;$

5. Calculation of the inner angles of the triangle using a Law of Cosines

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 24**2-30**2-30**2 }{ 2 * 30 * 30 } ) = 47° 9'23" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 30**2-24**2-30**2 }{ 2 * 24 * 30 } ) = 66° 25'19" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-24**2-30**2 }{ 2 * 30 * 24 } ) = 66° 25'19" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 329.95 }{ 42 } = 7.86 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24 }{ 2 * sin 47° 9'23" } = 16.37 ; ;$

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