Mathematics, 10.07.2019 04:30 ginareyes0423

From a point 80 feet in front of a library, the angles of elevation to the base of a flagpole, and to the top of the flag are 22° and 43.5°, respectively. find the height of the flagpole to the nearest foot.

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In this exercise we have to use the knowledge of trigonometry to calculate the closest point of the library, in this way we find that this value corresponds to:

Y= 44

Thus, we will first use the definition of tangent, which is given by:

$tan (\theta) = \frac{opposite}{adjacent}$

So looking at the figure informed, we can see that this formula can be rewritten as:

$tan(22^o )= \frac{x}{80} \\80 tan(22^o) = x$

Now using the new condition and writing in function of the other angle we find that:

$tan(43.5^o) \frac{x+y}{80}\\=80tan(43.5^o) = y+x \\=80tan(43.5^o)-x= y \\=80tan(43.5^o)-80tan(22^o) = y \\y= 44$

See more about trigonometry at link

From a point 80 feet in front of a library, the angles of elevation to the base of a flagpole, and t

Answer from: Sabby5069

check the picture below.

$\bf tan(22^o)=\cfrac{x}{80}\implies \boxed{80tan(22^o)=x}
\\\\[-0.35em]
~\dotfill\\\\
tan(43.5^o)=\cfrac{y+x}{80}\implies 80tan(43.5^o)=y+x\implies 80tan(43.5^o)-x=y
\\\\\\
80tan(43.5^o)-80tan(22^o)=y\implies 43.59506727037783689501 \approx y
\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
~\hfill \stackrel{rounded~up}{44=y}~\hfill$

make sure your calculator is in Degree mode.

Answer from: Quest

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

Which are the possible side lengths of a triangle?

Answer from: Quest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

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