Question

I have the answer but i dont know how..
The lower edge of a mural, 12 ft high, is 6ft above an observer’s eye. Under the assumption that the
most favorable view is obtained when the angle subtended by the mural at the eye is maximum, at
what distance from the wall should the observer stand?

Answer 1

we have the same drawing sir

Answer 2

From the lower small triangle
\[\tan(s) = \frac{6}{x}\tag{1}\]

From the big triangle
\[\tan(t+s)=\frac{18}{x}\tag{2}\]

Answer 3

Our goal is to eliminate \(s\) somehow and get an equation with \(t\) and \(x\) as variables

Answer 4

In view of that, apply the angle sum formula :
\[\large \tan(t)=\tan((t+s)-s)=\frac{\tan(t+s)-\tan(s)}{1+\tan(t+s)\tan(s)}\]

plugin the values

Answer 5

ok sir i will solve now

Answer 6

i got this sir: