Question

Vicky looked at the outside of a circular stadium with binoculars. She estimated the angle of her vision was reduced to 60º. She is positioned so that the line of site on either side is tangent to the stadium. What was the measure of the arc of the stadium intercepted by the lines of site?

Answer 1

notice the picture below

using the "far arc - near arc" equation, thus, solve for "x"

Answer 2

120º

Explanation:

When you have an outside angle, with the lines that form it being tanget to a Circle to be able to calculate the lenght of the arc of the circle, comparing to that angle you just have to use the formula that states that

Angle=
`(1)/(2) (Arc 2- Arc1)`

Since the angle is 60 we just have to put a different value for both the arcs, in this case the small arc will be x and the big arc will be 360-x, so now you have somethin like this:

60=
`(1)/(2) (360- x- x)`

120= 360- x- x

-240=-2x

x=
`(-240)/(-2)`

x=120