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?
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
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
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 ??
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
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.