The eastern alberta dc transmission line is a project that began construction in 2012. it includes a 500km, 500kv power line from the brooks area to the edmonton area. (the v stands for "volts", an si unit for electrical potential.)a. suppose the towers supporting the line are 1.5 hm apart. how many towers would be required to complete the project? b. a rechargeable aa battery produces approximately 1.2 volts. how many times larger is the voltage in the power line than that of the battery?

(a) The number of required towers is 3334.

(b) The voltage in the power line is or 416666.67 times of the power of battery.

Step-by-step explanation:

Given information: Length of power line is 500 km and voltage of power line is 500 kV.  (The V stands for "volts", an SI unit for electrical potential.)

(a)

It is given that the towers supporting the line are 1.5 hm apart.

We need to find the number of required towers.

1km = 10 hm

Therefore the number of required towers is 3334.

(b)

It is given that a rechargeable AA battery produces approximately 1.2 volts.

We need to find by how many times larger is the voltage in the power line than that of the battery.

1 kV = 1000 V

Therefore the voltage in the power line is or 416666.67 times of the power of battery.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4