Hi Martha,
I just read WyzAnt's academic honesty policy, and this sounds an awful lot like a homework question. I have an answer, but it would be better for you to set up this problem yourself.
Some of my students have trouble visualizing problems like these. I encourage you to create a diagram.
I drew a triangle with one vertical side representing the flag pole. We know the woman is standing above the bottom of the flag pole and below the top, so I drew a point off to one side representing her position that was roughly level with the middle of the vertical line segment. That's the third vertex of the triangle.
Then I drew one more line segment, a horizontal segment which starts at the woman's position and ends at the flag pole at a perpendicular intersection. I hope you can see that the length of this line segment is what we're trying to determine. Give it a variable name. I called it d.
The lengths of the flag pole above and below the horizontal line are not known. I called them x and y. But the sum of those two values is known, it's 70 feet. So I marked that on the drawing.
Finally, I labeled the 18-degree angle of elevation and the 14-degree angle of depression.
If you drew everything correctly, you now have enough information to write three equations for your three unknowns. Post those equations. I would ask you to post your drawing, but it doesn't appear that WyzAnt allows graphical attachments. Good luck.
