Expert: Josh - 5/22/2006

Question
hi again! this is my last question by the way.
ok, here goes:
   
     B
    /I
5  / I 3
  /  I
A /---I C
  4

(its suppose to be a triangle with 5 as the hypotenue 4 at the bottom, 3 at the sides. C is on the right angle, B is on the top, and A is across the right angle. i know its a bit confusing!)

In the above sketch, sin B has a value of:

A. 4/3
B. 4/5
C. 3/4
D. 3/5

thanks sooooooooo much for your help! :)  

Answer
Let x be the angle ^ABC.
sin(x) is the ratio between the opposite side (from the point of view of angle x) and the hypotenuse.

So, sin(x)=|AC|/|AB|=4/5

By the way, you can straight-away eliminate option A. The ratio |AC|/|AB| is always less than or equal to 1. This is because the term in the denominator (viz., |AB|) representing the hypotenuse can never be shorter than any other side in a triangle.