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Babynini
 one year ago
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.
Babynini
 one year ago
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.

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Babynini
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434728278112:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0(the drawing was not given to me, it is my representation of the question)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2I think that the right drawing is: dw:1434728792636:dw

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0hrrm, ok. I thought of that but didn't want to assume it was a right angle.

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0dw:1434728933190:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2then: h= x * tan(32)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2oops: h= x* tan(35)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Hm? why that? that's the second triangle

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0you mean after we solve for x in tan(32) = h/(1000+x) then we do h= x*tan(35) ??

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2yes! dw:1434729130312:dw

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2we 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
 one year ago
Best ResponseYou've already chosen the best response.2we have to solve the last equation for x

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0er well 1,000tan(32) = 624.87

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2\[x\tan 32 + 624.87 = x\tan 35\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0So why does that equal xtan35?

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2since you don't know the value of x

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0hm k. Now what do we do? :)

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2we 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
 one year ago
Best ResponseYou've already chosen the best response.2then dividing both sides by (tan35tan32), we get: \[x = \frac{{624.87}}{{\tan 35  \tan 32}} = ...\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2ok! Now substitute that value into this formula: \[h = 8294.2 \times \tan 35 = ...\]

Michele_Laino
 one year ago
Best ResponseYou've already chosen the best response.2since: \[h = x\tan 35\]

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0I plug it into that second one?

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0So 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
 one year ago
Best ResponseYou've already chosen the best response.2that's right, nevertheless it is 624.87 not 625.87

rvc
 one year ago
Best ResponseYou've already chosen the best response.0Thank you so much @Michele_Laino :)

Babynini
 one year ago
Best ResponseYou've already chosen the best response.0Oh, right. Sorry, that was a typo :P thanks!!
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