jmc

Question

A "slackrope walker" is much like a tightrope walker except that the rope on which he performs is not pulled tight. Paul, a slackrope walker, has a rope tied to two

15 m

high poles which are

14 m

apart. When he is standing on the rope

5 m

away from one of the poles, he is

3 m

above the ground. How long in meters is the rope?

Accepted Answer

Label the points A, B, C, and D, as shown. Through P, draw a line parallel to DC as shown. The points X and Y are where this line meets AD and BC. From this, we see that AX=BY=15-3=12. Also, PY=14-5=9. FIGURE To calculate the length of the rope, we need to calculate AP and BP, each of which is the hypotenuse of a right triangle. Now, AP^2=12^2+5^2=169 so AP=13, and BP^2=12^2+9^2 = 225, so BP=15. Therefore, the required length of rope is 13+15 or 28 m.