help geometry

Question

0

201

2

In the diagram, AOB is a sector of a circle with angle AOB = 60. OY is drawn perpendicular to AB and intersects AB at X. What is the length of AB?

Guest Jul 4, 2022

BuilderBoi · Answer 1 · 2022-07-04T06:06:37

Using the Law of Cosines on \(\triangle AOB\) gives us \(AB = \sqrt{20^2 + 20^2 - 2\times 20 \times 20 \cos 60} = \color{brown}\boxed{20}\)

CPhill · Answer 2 · 2022-07-04T06:23:19

Also.....notice that if angle AOB = 60

Then angle AOX = 30 = angle BOX

And angle OAB = Angle BOA = 60

So triangle AOB is equilateral with AB = 20