EXAMPLE 3.7.3

The figure below shows the Math Department's plan to run a computer cable (w) from the top of the Algebra Building (A) to the top of the Trig Tower (T). Find the total cost of the cable, assuming that it costs $3.50 per foot. (The front faces of the buildings, and the cable, are all in the same plane.)

 

A. $75

B. $21

C. $263

D. $753

SOLUTION

We need to find the length of the wire (in feet) and multiply by the cost factor of $3.50 per foot.

We can find the length of the wire by recognizing that the wire is the hypotenuse of a right triangle whose legs measure 60 feet and 45 feet respectively (the 45-foot height is obtained by subtracting the height of the Algebra Building from the height of the Trig Tower). Let L be the length of the wire. According to the Pythagorean Theorem,

L squared equals 60 squared plus 45 squared
L squared equals 3,600 plus 2,025
L squared equals 5625
L equals the square root of 5,625
L equals 75

The length of the wire is 75 feet, and the cost is $3.50 per foot, so the total cost is (75) times ($3.50) = $262.50. The best choice is C.