Find the lengths of the guy ropes. You’re chief engineer of Rivendell and Lord Elrond has assigned you the task of building a lookout tower. The tower will be build on a hill that has an inclination to the horizontal of 9 degrees. He wants there to be exactly 78 ft from ground to the base of the nest. The two guy ropes that support the tower are fastened to the base of the nest and then at two points on the hill that are each exactly 20 feet directly above and directly below the base of the main support post. These guy ropes are very expensive to build so you’ve been instructed to be very precise in calculating the total length of rope you need. Be within a tenth of a foot for the sum of both ropes. How much rope do you need?
*I have no idea how to do this one, so any help would be greatly appreciated*
Answers & Comments
The angle where the tower meets the hill in the right-side triangle is 90 + 9 = 99º
You have two sides and the included angle for the support rope on the right so use law of cosines (where support rope = c)
c² = 20² + 78² - (2 • 20 • 78 • cos 99) so solve for c
and on the other side, that angle is 90 - 9 = 81 so do it like the first one