Compute height of the Empire State Building

olusiart

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Aug 13, 2016
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Need some help with that task: Compute height of the Empire State Building using the information given in illustration 2.

attachment.php


attachment.php


I tried using the law of cosines and sines, also Pythagorean theorem but couldn't solve it. Thanks!
 

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Let A,B,C represent vertices of the larger right angle triangle where AC = 1340 ft ,
angle ABC = 90 deg, angle BCA = 34.4 deg
Let D,A,B represent vertices of the smaller right angle triangle where DA = h
(height of building), angle DAB = 90deg, ABD = 58.8 deg


Let's see if you can work out the height of the building by filling in the boxes.


Step 1 : Calculate AB using sin function
(working out OPPOSITE side given angle and HYPOTENUSE)
sin© = O/H where @ = 34.4 deg, H= 1340, O= AB
By substitution sin◻️= AB/◻️ => AB = sin◻️ x ◻️ => AB = ◻️


Step 2 : Calculate DA using tangent function
(working out OPPOSITE side given angle and ADJACENT side)
tan➰ = O/A where ➰ = 58.8 deg, O = DA, A = AB


By substitution tan◻️ = DA/◻️ => DA = tan◻️ x ◻️ => DA = ◻️
 
@Denis Well, that's the illustration I got from the teacher, so it's as messy and unclear for me as it is for you...

I'm from Poland and our 1's look like this, sorry for the inconvenience. Answering your "And how in heck did you come up with 34.4 = 6/1340?" - it's a small letter "B" not 6... I just marked this side as "b". And btw, I only added my drawing to be a better version of the original illustration, to make it bigger and clearer, not for the notes on the side. Don't pay attention to them.

@hoosie Thank you for your help. I know what my problem was now. I have done your "step one" but I didn't take both triangles as right triangles. That's why I added the right angle to the first (original) drawing. If I assume that both triangles (the larger ABC and the smaller DAB) are right then the task is very easy.

So that's what I have done now and the answer I got is 1250 feet. Is that what you got too? It actually is the height of the Empire State Building (but without the antenna spire) so I'm hoping that's correct.
:D

Thank you guys for your help and sorry for any mistakes and/or bad grammar. English is not my first language...
:(
 
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