Tower 1 is 60 ft high and tower 2 is 20 ft high. The towers are 140 ft apart. A guy wire is to run from point A to the top of each tower. [See a picture of this situation on page 274 of the textbook.]

Question

Tower 1 is 60 ft high and tower 2 is 20 ft high. The towers are 140 ft apart. A guy wire is to run from point A to the top of each tower. [See a picture of this situation on page 274 of the textbook.] 
How many feet from tower 1 should point A be so that the total length of guy wire is minimal? Do not include units in your answer. 
Distance from tower 1 to point A is???

Steve · Answer

without a diagram, I assume point A is an anchor in between the towers. If its distance from T1 is x, then the cable length is

d = √(60^2+x^2) + √(20^2+(140-x)^2)
to find the minimum, we want dd/dx = 0
That happens when x=105