Okay, so here is my problems:

1) Pinky measures that place is 100 feet wide, and the distance from the place of the tribune is 20 feet. Tribune angle he estimates to 45 degrees. He then draw a shape with a

triangle ABC where A is 90 degrees. Then he draws a line from C to a point D on AB such that

the length of AC is equal to the length of AD, then a line from C to a point E on DB

so that DE has length 20 and EB has length 100 The length of the segment CD called

he x. He draws out the angles ADC and DCA are both 45 ◦. Finally he lets

ECB called φ and θ called ACE.

a) Draw Pinky figure. Show that

tan(θ +φ) = 1 + (120√2)/x and tan θ = 1 + (20√2)/x

b) Find φ expressed as a function φ (x) of x for x ∈ (0,∞)

c) Find lim φ(x) if (x→0^{+}) and lim φ(x) if (x→∞)

d) Find φ(x) for x ∈ (0,∞), and determine where φ (x) grows and declines.

e) Assume that the king set so that the viewing angle φ (x) onto the space was maximal.

How many feet should the pirates go up the tribune to get to where the king sat?