How Far Should You Stand from the Statue of Liberty for the Best Viewing Angle?

[nvidia69]

Homework Statement

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?

Homework Equations

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

The Attempt at a Solution

I just don't understand what the largest viewing angle will be, wouldn't it just be the closest thing to 180 degrees? Also, wouldn't one theoretically be able to view all of the statue from any distance away?

 

[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

 

[Architeuthis Dux]

This problem seems to be missing some key information in order to properly solve it. Additionally, the Law of Sines may not be the most appropriate equation to use in this situation as it is typically used for solving triangles with known angles and sides. The Law of Cosines may be a better option as it can solve for angles and sides in non-right triangles. However, without more information, it is difficult to provide a definite solution to this problem.