Can you find the angle in this trigonometry problem?

[arthur.prior]

I'm having some difficulty with a trigonometry problem. Can anyone explain how I would be able to find the angle highlighted in red? I feel stupid

 

[lev888]

Look up how to find angles of a triangle with known sides.

 

[Dr.Peterson]

The best tool is the Law of Cosines.

 

[Deleted member 4993]

You know for the triangle OAB, AB = 4, OA =7.5 and OB = 10. Using law of cosines for triangle you can calculate angle OAB and from that the required angle. You can use the law of sines too - but the path to correct answer would be tortuous.

 

[Harry_the_cat]

@arthur.prior Perhaps you are missing the fact that the third side of the triangle is a radius of the circle and therefore 10 units.

 

[blamocur]

I'm having some difficulty with a trigonometry problem. Can anyone explain how I would be able to find the angle highlighted in red? I feel stupid

View attachment 30958

My $0.02 : once you figure out the hight of the triangle (point B in one of the posts) you can figure out the cosine of your angle.