Expert: Richard J. Raridon - 3/26/2007

Question
QUESTION: A surveyor sets up his theodolite some distance due south of a building and finds that the angle of the elevation of the top of the building is 42 degres.He then moves 98 meters due west and finds that the angle of the elevation is now 36 degrees the theodolite is 1.5 meters above the ground find the height of the building using scale drawing techniques can you please show me how to do this or how you would go about it please thankyou
ANSWER: Let h+1.5 = height of building, x = distance from 1st position to the building and y = distance from 2nd position to the building.  
tan42 = h/x and tan36 = h/y
x^2 +98^2 = y^2
1.2335h^2 +98^2 = 1.8944h^2 so h = 120.5m and the height
= 122m

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QUESTION: Richard please can you check the following because the way youve worked it out and the way i worked it out are totally different please advise which one is right
this is what i have done

tan 36 x 98 = 71.20116774
then i took that answer and did
tan 42 x 71.20116774 = 64.10981939
then i added 1.5 this brings it to 65.60981939
the height of the building would be 65.6 m
is this right or is your answer right please take a second look and let me know thankyou very much

ANSWER: 98 is not in the direction of the building with the angle 36 degrees.  I feel confident in my answer.

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QUESTION: please could you go through step by step how you got to your answer and also how i would draw this to a scale drawing please regards
ANSWER: Draw a right triangle.  The base is 98, the right side is x and the hypotenuse is y.  So x^2 +98^2 = y^2.  
x = h/tan42 and y = h/tan36.  Square those values and put them in the first equation as I did.  Solve for h.  Then you can also calculate x and y and make your scale drawing.

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QUESTION: im sorry to be thick but i need to know how to calculate them x,y
so how do you do x=h/tan 42 and y= h/tan 36 and how do you solve for h
ANSWER: Can you find the tangent of 42 degrees with your calculator?  x = h/tan42 = 1.1106h so x^2 = 1.2335h^2
y = h/tan36 = 1.3764h so y^2 = 1.8944h^2
Substitute those into x^2 +98^2 = y^2 and solve for h.

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QUESTION: i can find tan 42 it comes out at 0.900404044
what does x = h/tan 42 does it mean height divided by tan 42 and how do you get to 1.1106h and how does x squared = 1.2335h squaredand how do i substitute int that equastion please can you make it any clearer pleaseeeeeeee

Answer
Obviously, x = h/tan42 means divide h by tan42 and 1 divided by 0.9004 = 1.1106
so you have x = 1.1106h and if you square both sides you have x^2 = (1.1106^2)h^2, is that so hard?
If you can't figure out how to substitute that into
x^2 +98^2 = y^2, I can't help you further.