Math Is Fun Forum

ninjaman

Member

Registered: 2013-10-15

Posts: 61

wording of a question and showing answer

hello

I completed the answer for this question some time ago but I cant remember the start of it which I didn't write down. please could someone confirm what I have so far.

this is the question

form a ship at sea, the angles of elevation of the top and bottom of a vertical lighthouse standing on the edge of a vertical cliff are 31 degrees and 26 degrees respectively. if the lighthouse is 25m high, how high is the cliff?

H is height in meters (of cliff)

H + 25 / tan 31= H / tan 26, this is how I started the formula. should I add + 25 to the H + 25 / tan 26?

(H + 25) tan 26 = H tan 31

H + 25 tan 26 = H tan 31

H tan 26 + 25 tan 26 = H tan 31

25 tan 26 = H tan 31 - H tan 26

25 tan 26 = H (tan 31 - tan 26) this second bit works out to 0.1131280305, I divided the second bit by this to move it across the equals sign

25 tan 26 / 0.1131280305 = 107.8 (rounded up)

does this make any sense to anyone?
I cant remember how I started it. I have the rest written down.

Christmas soon!!!

all the best
simon:)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: wording of a question and showing answer

Hi;

That is the same question from over here:

http://www.mathisfunforum.com/viewtopic.php?id=20223

Merry Christmas!

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

irspow

Member

Registered: 2005-11-24

Posts: 1,055

Re: wording of a question and showing answer

If L=lighthouse height, C=cliff height, and x=distance from ship to cliff and lighthouse

tan31=(L+C)/x  and

tan26=C/x  solve for x in this one

x=C/tan26  plug this into first equation

tan31=[(L+C)tan26]/C

Ctan31=Ltan26+Ctan26

Ltan26=C(tan31-tan26)

C=Ltan26/(tan31-tan26)

C=107.78m

So your answer seems good.  The above is just how the problem struck me.  I just noted the two ratios and used two equations with two unknowns.  It seemed pretty straightforward.  You did the same thing which worked out fine.  The only thing that I did different was to not calculate any values until the very end, because I didn't need them until then to solve for the height of the cliff.  (I do this a lot because it keeps small rounding errors from getting very large in problems with many steps.)

Oh, and now we know how far the ship is from the lighthouse too...LOL

x=C/tan26    or more precisely because C was rounded

x=L/(tan31-tan26)

x=220.99m

Last edited by irspow (2013-12-24 01:39:04)

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I am at an age where I have forgotten more than I remember, but I still pretend to know it all.