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J and s are facing each other on opposite sides of a 10 m flagpole. From j pov the top of the pole is at an angle of elevation of 50 degree. From S pov is 35 degree. How far apart are j and S?

 Dec 15, 2017
 #1
avatar+111329 
+2

J and S are facing each other on opposite sides of a 10 m flagpole. From j pov the top of the pole is at an angle of elevation of 50 degree. From S pov is 35 degree. How far apart are j and S?

 

Note that, from J's point of view

 

tan (50)  = 10 / D1       where D1 is the distance J is from the pole

 

And from S's point of view

 

tan (35)  =  10 / D2        where D2  is the distance S is from the pole

 

So.....rearranging both......their distance apart is given by :

 

D1   +  D2  =

 

10/tan(50)   +  10/tan(35)    ≈  22.67 m

 

 

cool cool cool

 Dec 15, 2017
 #2
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I got a question... when do you know when to divide tan or when to bring the opposite or adjacent over to multiple? I'm confused on that and btw thanks

Guest Dec 15, 2017
 #3
avatar+111329 
+2

Note that the tangent of an angle  is the opposite / adjacent

 

So.....consider the flagpole height the opposite side and the distance to the flagpole , D, is the adjacent side

 

So....

 

tan x  =   10  / D           multiply both sides by D

 

D *  tan x  =  10          divide both sides by tan x

 

D  = 10  / tan x

 

 

Does that make sense ??

 

 

cool cool cool

 Dec 15, 2017
edited by CPhill  Dec 15, 2017
 #4
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Not really

Guest Dec 15, 2017
 #5
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Okay so to find distance, we have to divide and to find length/height we have to multiple, correct?

Guest Dec 15, 2017
 #6
avatar+8962 
+1

Maybe this will help:

The bottom of the flag pole is point  A .

 

In every right triangle,  tan(angle)  =  length of opposite side / length of adjacent side. So....

 

tan( 50° )  =  10 / JA          Solve this equation for  JA  to get:          JA  =  10 / tan( 50° )

 

tan( 35° )  =  10 / SA         Solve this equation for  SA  to get:          SA  =  10 / tan( 35° )

 

JS  =  JA + SA                  Plug in the values we just found for  JA  and  SA .

 

JS  =  10 / tan( 50° )  +  10 / tan( 35° )

 

JS  ≈  22.67  meters

 

------------------------------

 

when do you know when to divide tan or when to bring the opposite or adjacent over to multiple?

 

Think about this problem:

 

8  =   16 / x     To solve for  x  , first multilply both sides by  x .

8x  =  16         Then divide both sides by  8  .

x  =  2

 

Similarly....

 

tan x  =   10  / D     To solve for  D  , first multiply both sides by  D .

D * tan x  =  10       Then divide both sides by  tan x  .

D  =  10 / tan x

 

Remember that  tan x  is just a number.

 Dec 15, 2017
 #7
avatar+111329 
+1

Thanks, hectictar  !!!!

 

 

cool cool cool

 Dec 15, 2017

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