# Homework Help: Law of Sines word problem

1. Jan 4, 2010

### nvidia69

1. The problem statement, all variables and given/known data
The statue of libery is 46 meters tall and stands on a plinth 47 meters tall.
How far back should a 2m tall person stand back to obtain the largest viewing angle? There is 66m of land in front of the statue, will the position be within these 66 meters?

2. Relevant equations
Law of Sines: sina/A=sinb/B
Law of cosines: b^2=a^2+c^2-2ac(cosB)

3. The attempt at a solution

I just dont understand what the largest viewing angle will be, wouldnt it just be the closest thing to 180 degrees? Also, wouldnt one theoretically be able to view all of the statue from any distance away?

2. Jan 4, 2010

### mgb_phys

Easiest way might be to try an answer for few values of distance.
hint - assume the statue and plinth are a straight line.

So if you are 1m from plinth you have a narrow angle between a triangle of base 46m starting 45 away
Then try at 66m and then 30m, 40m, 50m and see what the trend is.

hint, if you haven't done much trig you might want to make it a right angle triangle and then find 'A' by working out the total angle and the angle just below A