Answer: 12 feet
Explanation:
I'm assuming the rope is fully taut and connects the top of the flag pole with the tip of the shadow.
Draw a right triangle that has a horizontal leg of 5 feet and a hypotenuse of 13 feet. I'll call these a = 5 and c = 13.
Use the pythagorean theorem to find b
[tex]a^2 + b^2 = c^2\\\\5^2 + b^2 = 13^2\\\\25 + b^2 = 169\\\\b^2 = 169-25\\\\b^2 = 144\\\\b = \sqrt{144}\\\\b = 12[/tex]
The vertical leg of the right triangle is 12 feet, which is the height of the flag pole. We have a 5-12-13 right triangle.
