HELP! :( My assignment in maths is hard :(

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?

Re: HELP! :( My assignment in maths is hard :(

Part 1 appears to be translated from another language, making it difficult to read. What is "that place"? How does it relate to the triangle ABC? What does "the distance from the place of the tribune" mean? What is a tribune angle?

Anyway, from the rest of the problem, to get you started: you know that triangle ADC is a 45-45-90 triangle. Since its hypotenuse has length x, the sides $\displaystyle |\overline{AC}| = |\overline{AD}| = \frac{x}{\sqrt{2}}$. Then,

$\displaystyle \tan\theta = \dfrac{\text{opp}}{\text{adj}} = \dfrac{|\overline{AE}|}{|\overline{AC}|} = \dfrac{\left(\dfrac{x}{\sqrt{2}} + 20\right)}{\left(\dfrac{x}{\sqrt{2}}\right)} = 1 + \dfrac{20\sqrt{2}}{x}$

Can you do the rest?

Re: HELP! :( My assignment in maths is hard :(

Thank you so much, it really helped :D

And sorry for the translation, i'm not the best english writer.. :P