Babynini
  • Babynini
Height of a mountain To estimate the height of a mountain above a level plain, the angle of elevation to the top of the mountain is measured to be 32 degrees. One thousand feet closer to the mountain along the plain, it is found that the angle of elevation is 35 degrees. Estimate the height of the mountain.
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Babynini
  • Babynini
|dw:1434728278112:dw|
Babynini
  • Babynini
@rvc free?
Babynini
  • Babynini
@zepdrix :)

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

Babynini
  • Babynini
@Michele_Laino
Babynini
  • Babynini
(the drawing was not given to me, it is my representation of the question)
Michele_Laino
  • Michele_Laino
I think that the right drawing is: |dw:1434728792636:dw|
Babynini
  • Babynini
hrrm, ok. I thought of that but didn't want to assume it was a right angle.
Babynini
  • Babynini
|dw:1434728933190:dw|
Babynini
  • Babynini
right?
Michele_Laino
  • Michele_Laino
yes! correct!
Michele_Laino
  • Michele_Laino
then: h= x * tan(32)
Michele_Laino
  • Michele_Laino
oops: h= x* tan(35)
Babynini
  • Babynini
Hm? why that? that's the second triangle
Babynini
  • Babynini
you mean after we solve for x in tan(32) = h/(1000+x) then we do h= x*tan(35) ??
Michele_Laino
  • Michele_Laino
yes! |dw:1434729130312:dw|
Michele_Laino
  • Michele_Laino
we have the subsequent step: \[\begin{gathered} \left( {x + 1000} \right)\tan 32 = h = x\tan 35 \hfill \\ \hfill \\ \left( {x + 1000} \right)\tan 32 = x\tan 35 \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
we have to solve the last equation for x
Babynini
  • Babynini
er well 1,000tan(32) = 624.87
Michele_Laino
  • Michele_Laino
ok! correct!
Michele_Laino
  • Michele_Laino
\[x\tan 32 + 624.87 = x\tan 35\]
Babynini
  • Babynini
So why does that equal xtan35?
Babynini
  • Babynini
and not h
Michele_Laino
  • Michele_Laino
since you don't know the value of x
Babynini
  • Babynini
hm k. Now what do we do? :)
Michele_Laino
  • Michele_Laino
we have to subtract x*tan(32) from both sides, so we get: \[\begin{gathered} 624.87 = x\tan 35 - x\tan 32 \hfill \\ \hfill \\ 624.87 = x\left( {\tan 35 - \tan 32} \right) \hfill \\ \end{gathered} \]
Michele_Laino
  • Michele_Laino
then dividing both sides by (tan35-tan32), we get: \[x = \frac{{624.87}}{{\tan 35 - \tan 32}} = ...\]
Babynini
  • Babynini
8294.19 !
Babynini
  • Babynini
ft
Michele_Laino
  • Michele_Laino
ok! Now substitute that value into this formula: \[h = 8294.2 \times \tan 35 = ...\]
Michele_Laino
  • Michele_Laino
since: \[h = x\tan 35\]
Babynini
  • Babynini
I plug it into that second one?
Babynini
  • Babynini
= 5807.7 ft
Michele_Laino
  • Michele_Laino
that's right!
Babynini
  • Babynini
yayaya :)
Michele_Laino
  • Michele_Laino
:)
Babynini
  • Babynini
So what we did: tan(32) = h/(1000+x) (1000+x)tan(32)=h xtan32+625.87 = xtan(35) subtract xtan(32) from both sides 625.87 = xtan(35)-xtan(32) 625.87 = x(tan(35)-tan(32)) divide the 625 by the tans to get x = 8294 plug that into h=xtan(25) to get our result 5808ft
Michele_Laino
  • Michele_Laino
that's right, nevertheless it is 624.87 not 625.87
rvc
  • rvc
Thank you so much @Michele_Laino :)
Michele_Laino
  • Michele_Laino
:) @rvc
Babynini
  • Babynini
Oh, right. Sorry, that was a typo :P thanks!!
Michele_Laino
  • Michele_Laino
thanks!!

Looking for something else?

Not the answer you are looking for? Search for more explanations.