Albert lives in the southern us. at noon on a summer day, the angle of elevation of the sun is 83.5 degrees. the window in albert's room is 4.0 feet high and 6.5 feet wide and the wall is 6 inches thick. determine the area of the floor surface in albert's room that is illuminated by the sun.

Calculate the volume, that is easy: 

4 x 5 x 2.5 = 50m3 

now, as you did not provided if you use nitrogen in 

ntp (normal temperature and pressure - 20c, 1atm) weight is 1.165kg/m3 

or: 

stp (standard temperature and pressure - 0c, 1atm) weight is 1.2506 

these are in case of pure nitrogen, as in presented case nitrogen is only 79% we need to change weights to represent that: 

ntp - 1.165kg/m3 / 100% x 79% = 0.92035kg/m3 

stp - 1.2506kg/m3 / 100% x 79% = 0.987974kg/m3 

therefore in case of: 

ntp, total weight of n2 will be 50m3 x 0.92035kg/m3 = 46.0175kg 

stp, total weight of n2 will be 50m3 x 0.987974kg/m3 = 49.3987kg

If we draw a sketch based on the problem, we would come up with two similar right triangles. We can then solve the problem by ratio and proportion. If we let x as the width of the illuminated part of the floor, then we have the equation:
0.5 / (0.5 + x) = x tan 83.5 / (4 + x tan 83.5)
Solving for x
x = 0.477 ft

Therefore, the area of the illuminated part of the floor is:
0.477 ft x 6.5 ft = 3.10 sqr. ft.