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a surveyor with a 6 foot transit measures a 12 degree angle of depression from the top of a building he is on, to the top of another building that he knows is exactly 245 feet away (horizontally). if the building he is on is 54 feet tall, how tall is the other building

 Jan 31, 2017
 #1
avatar+36923 
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TAN = opp/adj    opp is the height above him .....

added to his building height and the 6 foot transit will give the other building height

 

tan 12 = opp/245     opp = 245 x tan12 = 245*tan(12 = 52.07635760915   then add building and transit height                 + 54  +6 = 112.076 ft tall

 Feb 1, 2017
edited by ElectricPavlov  Feb 1, 2017
edited by ElectricPavlov  Feb 1, 2017
 #2
avatar+36923 
0

CORRECTION  .....I misread the question (I thought it was angle of ascension)....asinus probably has it correct

 

Tangent 12 = opp/245 

opp = tan12  * 245 = 52.076      

54 +6 - 52.076 = 7.924 ft tall      (asinus calc a little off)

 Feb 1, 2017

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