Express answers in simplest exact form.

An equilateral triangle with side of 2sqrt3 is inscribed in a circle. What is the area of one of the sectors formed by the radii to the vertices of the triangle?

Question

Express answers in simplest exact form.

An equilateral triangle with side of 2sqrt3 is inscribed in a circle. What is the area of one of the sectors formed by the radii to the vertices of the triangle?

anonymous · Answer

angle should be 360/3 =120 
then there is some formula which i don't remember sorry : (

anonymous · Answer

If you draw this as a picture you will note that a line from the center of the circle to any of the corners of the trianngle is the radius. This makes an obtuse triangle. If you split the 3 triangles in 2 you get some right triangles to work with. The angles of these triangles are 30-60-90. The adjacent side to the 30 degree angle is sqrt3. This allows us to solve the hypotenuse or radius:
$$cos(30) = \sqrt {3}/x $$
$$x= \sqrt{3}/cos(30)$$
$$x=2$$
Area of circle = 2 pi r
Area of sector = 2/3 pi r
Area of sector = $$(2/3) \pi (2) = (4/3) \pi$$

anonymous · Answer

so it 4/3?

anonymous · Answer

It's 4/3 pi
The pi matters :)
Sorry been working an integral and was preoccupied :P