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?

Guest Dec 15, 2017

#1**+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

CPhill
Dec 15, 2017

#3**+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 ??

CPhill
Dec 15, 2017

#6**+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

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*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.

hectictar
Dec 15, 2017