16 28 28 triangle

Acute isosceles triangle.

Sides: a = 16 b = 28 c = 28

Area: T = 214.663252584
Perimeter: p = 72
Semiperimeter: s = 36

Angle ∠ A = α = 33.2033099198° = 33°12'11″ = 0.58795034029 rad
Angle ∠ B = β = 73.3988450401° = 73°23'54″ = 1.28110446254 rad
Angle ∠ C = γ = 73.3988450401° = 73°23'54″ = 1.28110446254 rad

Height: h_a = 26.833281573
Height: h_b = 15.333303756
Height: h_c = 15.333303756

Median: m_a = 26.833281573
Median: m_b = 18
Median: m_c = 18

Inradius: r = 5.963284794
Circumradius: R = 14.6098977453

Vertex coordinates: A[28; 0] B[0; 0] C[4.57114285714; 15.333303756]
Centroid: CG[10.85771428571; 5.111101252]
Coordinates of the circumscribed circle: U[14; 4.1743993558]
Coordinates of the inscribed circle: I[8; 5.963284794]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.7976900802° = 146°47'49″ = 0.58795034029 rad
∠ B' = β' = 106.6021549599° = 106°36'6″ = 1.28110446254 rad
∠ C' = γ' = 106.6021549599° = 106°36'6″ = 1.28110446254 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.

$a = 16 ; ; b = 28 ; ; c = 28 ; ;$

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

$p = a+b+c = 16+28+28 = 72 ; ;$

2. Semiperimeter of the triangle

$s = fraction{ o }{ 2 } = fraction{ 72 }{ 2 } = 36 ; ;$

3. The triangle area using Heron's formula

$T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 36 * (36-16)(36-28)(36-28) } ; ; T = sqrt{ 46080 } = 214.66 ; ;$

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

$T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 214.66 }{ 16 } = 26.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 214.66 }{ 28 } = 15.33 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 214.66 }{ 28 } = 15.33 ; ;$

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

$a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 16**2-28**2-28**2 }{ 2 * 28 * 28 } ) = 33° 12'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 28**2-16**2-28**2 }{ 2 * 16 * 28 } ) = 73° 23'54" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-16**2-28**2 }{ 2 * 28 * 16 } ) = 73° 23'54" ; ;$

6. Inradius

$T = rs ; ; r = fraction{ T }{ s } = fraction{ 214.66 }{ 36 } = 5.96 ; ;$

7. Circumradius

$R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 16 }{ 2 * sin 33° 12'11" } = 14.61 ; ;$

Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.