Geometry- Trigonometry question

Question

So I’m struggling to understand how to find the angle in this circle, we’ve recently learnt about trigonometry and like finding the area of a circle and all that but I can’t seem to remember which formula I have to use to find this angle. Can anyone lend a helping hand?

Answer 1

You can use the theorem of cosines: $$10^2=7^2+7^2-2\cdot 7^2\cos(\angle{AOB})$$

Answer 2

You can bisect the angle AOB, which divides isosceles triangle AOB into two right triangles. Each one of these right triangles has a hypotenuse of 7 and a leg of 5, so the sine of their angle at O is 5/7. As such, the measure of angle AOB is 2*arcsin(5/7).

Answer 3

You have an isosceles triangle with two sides as the radius of 7. This is because they tell you O is the center. Then you have $\sin(\theta/2)=5/7$. So the angle is $\sin^{-1}(5/7)*2$