SOLUTION: A flag pole XY of length 12m tilts towards an observation point A at an angle of 2° to the vertical. If A is on the same level as the foot, X, of the flagpole and /AX/=10m,find th

Algebra ->  Test -> SOLUTION: A flag pole XY of length 12m tilts towards an observation point A at an angle of 2° to the vertical. If A is on the same level as the foot, X, of the flagpole and /AX/=10m,find th      Log On


   

Question 1135196: A flag pole XY of length 12m tilts towards an observation point A at an angle of 2° to the vertical. If A is on the same level as the foot, X, of the flagpole and /AX/=10m,find the angle of elevation of the top of the flag pole from A, to the nearest degree.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A flag pole XY of length 12m tilts towards an observation point A at an angle of 2° to the vertical.
If A is on the same level as the foot, X, of the flagpole and AX = 10m,
find the angle of elevation of the top of the flag pole from A, to the nearest degree.
:
X = 90-2 = 88 degrees
:
Y
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12
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X---10---\A
:
find the side opposite X, call it x, using the law of cosines
x^2 = 12^2 + 10^2 - 2(12*10)*cos(88)
x^2 = 244 - 2(120)*.0349
x^2 = 235.624
x = sqrt%28235.624%29
x = 15.35 meters
:
Find angle A using the law of sines
15.35%2Fsin%2888%29 = 12%2Fsin%28A%29
cross multiply
sin(A)*15.35 = 12*sin(88)
sin(A) = 11.9927%2F15.35
A = 51.38 ~ 51 degrees