To find the distance AB across a river a distance BC of 673m is laid off on one side of the river. It is found that B=106.4degrees and that C=15.9degrees. Find AB
a) 181m
b) 221m
c)184m
d)218m

Question

anonymous · Answer

I just really need this explained

anonymous · Answer

This is what I picture: |dw:1323920382805:dw| So, we're given a nonhypotenuse side and told to find the other nonhypotenuse side. We know the two sides we're dealing with are not hypotenuses because point B is a component of both the sides we are dealing with, yet B has such a large angle that the side OPPOSITE it must be the hypotenuse (since all the angles in a triangle total to 180 degrees and B is large at 106.4 degrees). So, the sides which form a vertex at point B will follow an opposite/adjacent relationship. We're given the angle at point C, which is opposite of side AB. We can proceed from there:

$$AB = BC \times \tan (15.9^{o})$$