Christian is between two buildings. He stands 10 meters away from the taller building. If the angle of the top of the buildings from where he stands bears N8degreesW for the taller building and N10degreesE for the other. How far is he from the other building if the taller building is five-fourths as tall as the other?

Did you make a quick sketch?

First find the height of the taller building.
Using this and the fact that that height is 5/4 as tall as the shorter building, find the height of the smaller building.
Then, use the height of the smaller building and the angle that you have to get the distance that Christian is from the smaller building.