Machine trig

[Sabi]

Hey all I'm working through an engineering math book and this question has me stumped. Any pointers of how to approach it?

The questions are to find angle theta and dimension A

 

[Dr.Peterson]

Hey all I'm working through an engineering math book and this question has me stumped. Any pointers of how to approach it?

The questions are to find angle theta and dimension A

View attachment 22627

I might start by finding the horizontal and vertical distances between the centers of the two small circles. (This will not be hard at all.) From that, you can find the slope of the slanted line, which will give you the angle.

 

[Sabi]

I might start by finding the horizontal and vertical distances between the centers of the two small circles. (This will not be hard at all.) From that, you can find the slope of the slanted line, which will give you the angle.

Thank you

 

[Sabi]

I might start by finding the horizontal and vertical distances between the centers of the two small circles. (This will not be hard at all.) From that, you can find the slope of the slanted line, which will give you the angle.

Clearly overthinking it, as you said was easy, angle came out at (65.772°) which is correct. Any tip on the points to take for the next step finding the the distance across A?

I've tried to do it using right triangles but I'm not getting a way to hit the point I need. To then have a dimension i can deduct from the 86.29. I assume that's what I need to do?

 

[Dr.Peterson]

Clearly overthinking it, as you said was easy, angle came out at (65.772°) which is correct. Any tip on the points to take for the next step finding the the distance across A?

I've tried to do it using right triangles but I'm not getting a way to hit the point I need. To then have a dimension i can deduct from the 86.29. I assume that's what I need to do?

One approach could be to write an equation for the slanted line. Geometrically, I might find the position of the point of tangency on the lower circle (a little right-triangle trig, now that you have the angle), and then find the point of the intersection point you need, relative to that.