Apole that is 3.1m tall casts a shadow that is 1.46m long. at the same time, a nearby building casts a shadow that is 36.75m long. how tall is the building?

You have to find the angle of sunlight and the pole , which then cast a shadow
length of the pole is equal to 3.1m
creating a hypotenuse of 4.52m
the angle will be
[email protected] = opposite side / hypotenuse
= 1.46/4.52
= 0.32 that's 18.66 °
now for the building sin18.66° = opposite/hypotenuse
0.32 = 36.75/ hypotenuse
hypotenuse = 114.84 m
thus using Pythagoras theorem
114.84*114.84 = 36.75*36.75 + x^2
which comes around = 108.8 roughly 109 metres long

 
Do you remember hearing that the angles of every triangle in the world
all add up to the same number ?  They always add up to 180 degrees.

If you know the measures of two of the angles, then just take those away
(subtract) from 180 degrees, and whatever you have left must be the last angle.

For example, let's take the last one on your list:

54 and 36 are given.

       180 minus 54 = 126
then
       126 minus 36 = 90 . . ==> the missing angle is 90 degrees

Another way to do it:  One addition and one subtraction.

(54 + 36) = 90      That's the total amount you have to take away from 180.

180 minus 90 = 90  <== that's the missing angle.