Question

help
The screen in a theatre is 22 ft high and is positioned 10 ft above the floor, which is flat. The first row of seats is 7 ft from the screen and the rows are 3 ft apart. You decide to sit in the row where you get the maximum view, that is, where the angle theta subtended by the screen at your eyes is a maximum. Suppose your eyes are 4 ft above the floor, and you sit at a distance x from the screen.

a) Show that Theta = arctan(28/x) - arctan(6/x)

b) Use the subtraction formula for tangent to show that Theta = arctan(22x/(x^2) + 168)

Answer 1

I don't know how you have that equation, to me, I solve it on simple way and get the position is at the seventh row.

Answer 2

i completely have no clue how to even start this thing plz help me be on track

Answer 3

oh, I know my mistake, let me think more.

Answer 4

ok

Answer 5

hmm getting it now

Answer 6

@dumbcow @hartnn please, I am out of battery, this stuff is tough, please, help

Answer 7

@Loser66 , i think you over complicated the problem
using the diagram
\[\tan \theta_2 = \frac{6}{x}\]
\[\tan \theta_1 +\theta_2 = \frac{28}{x}\]
thus
\[\theta_1 = \tan^{-1} \frac{28}{x} - \tan^{-1} \frac{6}{x}\]

Answer 8

then to maximaize angle , take derivative , set equal to 0 and solve for "x"

Answer 9

oh yea, you are right!! my bad, I didn't see the link between x and theta.

Answer 10

and I thought that we can get particular solution for this, no need to generalize the form, @magepker728 terribly sorry, misguide.

Answer 11

its all good that is why im here to get some help :d thanks