Tanα=y/x
y=xtanα, we are told that x=25ft and α=30°
y=25tan30° ft
y≈14.43 ft (to nearest hundredth of a foot)
Since their home is 20 feet from the base of the tree, it poses no risk right now.
The rule for g(x) is: 
Step-by-step explanation:
Given function is:

When a function f(x) is shifted right or left, b units the new function is written as:

Shifting right

Shifting left

Similarly, when shifting up or down

As our given function is shifted 3 units to the right, it will be written as:

The function is when moved down 3 units, then

Hence
The rule for g(x) is: 
Keywords: Function transformation, Functions
Learn more about functions at:
#LearnwithBrainly
Distance from base = 305 / tan(29.5deg)
= 539 ft
The missing reason to complete Hector's proof is
<span>Corresponding Parts of Congruent Triangles Are Congruent
It's been established in the previous statement that triangle LNO and triangle PNM are congruent by the AAS Postulate.
The proof
</span>Corresponding Parts of Congruent Triangles Are Congruent
is comprehensive.
The domain is all real numbers except kπ, where k is an integer.
The range is (-∞, -1] ∪ [1, ∞)
Vertical asymtote is kπ, where k is an integer.