two vertical poles are 14 feet apart. one is 16 feet tall, and the other is 9 feet tall. A rope extends frim the top of one pole to the top of the other. Find how long the rope is.

Answer 1

Best way to draw a picture, you might have to do this using my explanation.

Let's name first pole AB, A is the point on the ground, B is the point on the top. We know that AB=16.

Let's name second pole CD, C is the point on the ground, D is the point on the top, we know that CD=9.

We also know that the distance between the two poles is 14, which means AC=14.

Imagine a rope which starts in top on first pole (at point B) goes to top of second pole (at D) and continue that rope until it hit the ground at one point. Let's call this point O.

If you draw a picture you will have two right triangles: ABO (m(A)=90) and CDO (m(C)=90), and you also have first pole is parallel to second pole or AB||CD.

Since AB||CD we have to similar triangles ABO and CDO. Two triangles are similar if and only if their corresponding side are proportional, which in our case means OC/OA=CD/AB=OD/OB.

But we do not know OC, let's call it OC=x. using first set of proportions we get

x/(x+14)=9/16

If you solve this equation you find that x=18 or OC=18

From the right triangle OCD using Pythagoras theorem you can find OD. Similar from the triangle ABO using Pythagoras theorem you can find OB.

Finally subtract OD from OB to find you rope distance from top of tall pole to top of small pole

Answer 2

The correct answer to this question is that the rope will form a catenary and you actually need some additional information to calculate its length...but I suspect that the answer wanted is that the rope will form a straight line which is the hypotenuse of a right triangle with sides 7 and 14...and you should know how to use the Theorem of Pythagoras to get the answer.