Question

I just rlly don't have a clue how I should proceed with this question.

A picture is hanging 3 meters high and is hanging so the bottom of the picture is 1 meter above you eye level. How far from the wall on which the picture is hanging should you stand so that the angle of vision occupied by the picture is (pi/6)

I know that you draw a triangle which is divided into a 3m part and 1m part. The non-right 3m triangle has angle (P) (pi/6) and the right triangle with 1m has angle (P) as theta. I have to use compound angle identities. But how?

Answer 1

Let

x = the distance from the wall
a = angle of elevation of the bottom of the picture
b = angle subtended by the picture

Then we have

1/x = tan(a)
4/x = tan(a+b)

we want b = pi/6. So,

(tana + tanb)/(1-tana*tanb) = 4/x

Now just plug in 1/x for tan(a) and solve for x