A flagstaff broke a second time. Previously , it broke @ a level 3 feet lower. The top of the staff touches the ground 6 foot from the bottom. Previously , it was 12 feet from the base. How tall is the flagstaff ?
No diagram was given. Should right ang triangles be used?
No picture? Yeesh! They're expecting a lot of assumptions, then. :-?
Yes, right triangles will likely be the way to go. I'd assume that, when they talk about the "top of the staff" "touching the ground" a certain distance from "the bottom", they mean us to gather that the upper portion (above the break) is still kind-of attached, with the broken-off bit clinging to the upright remainder of the pole at the break point, and the tip in the dirt, with the broken-off part being slanty sideways, forming the hypotenuse of the right triangle.
So your triangle for the current break could have "h" for the height (of the remaining upright portion), "6" for the base (along the ground), and, say, "L" for the length of the broken-off bit.
Your triangle for the previous break could have "h - 3" for the height, "12" for the base, and -- because the hypotenuse and the height together form the total length of the unbroken pole -- "L + 3" for the hypotenuse.
This gives you two equations in two unknowns. Solve the system, and back-solve for the value they want.
