What AP or Bridge are you planning on using?
Is 45' high enough to provide you with a minimum of 60% of the fresnel zone?
What is the distance between antennas, have you allowed for the curvature of the earth in your height calculation?
What kind of antenna are you planning on using? What gain does it have?
I would recommend a yagi or better yet a dish type.
Have you calculated your required gain and eirp to get back to your AP at the required data rate?
What is your acceptable link loss/ free space loss?
There are other things to take into account as well before going to the trouble of installation of a mast.
I'm not trying to pour cold water on your idea, but to be successful with this you need to be sure of a few things before you go to all the trouble of erecting a mast and making the investment.
Wireless AP's or Bridges often have more than one way to power them, is PoE the only possibility with your AP/ Bridge?
Normally the only cables running on the mast would be the antenna coax, no power goes to the mast. The AP or Bridge is inside a cabinet or building well away from extremes of heat and weather.
My last points would be simply to make absolutely certain that you have two Fibre Tranceivers and at least 1 meter of fiber cable in the ethernet link back to your house. Make sure you also fit a lightning arrestor to the antenna and ground the mast.
Of course the fiber will only be required if you are running a cable back to the house, if you are planning on using the AP/ Bridge in repeater mode you won't need the fibre, but understand that in repeater mode, your throughput will be drastically reduced.
In repeater mode, you also have the added complexity that will bring to take into consideration. Would probably be better to use 2 powered hubs and ethernet segments back to the house and use your PoE idea to power them.
I hope this gives you some food for thought...
rgds