SOLUTION: Please help. Sorry i didn't know what category to put this under. suppose you are standing 500 ft away from atree and you see a hawk hovering directly above that tree. the

Algebra ->  Radicals -> SOLUTION: Please help. Sorry i didn't know what category to put this under. suppose you are standing 500 ft away from atree and you see a hawk hovering directly above that tree. the       Log On


   

Question 141180: Please help. Sorry i didn't know what category to put this under.

suppose you are standing 500 ft away from atree and you see a hawk hovering directly above that tree. the angle of elevation from you to the hawk is 24 degrees. to the nearest foot, at what height is the hawk hovering.
thanks so much
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
This should come under the heading of trigonometry.
If you were to draw a diagram of this situation (always recommended) you would have a right triangle in which the distance from you to the base of the tree (500 ft.) is represented by the base of the triangle and the perpendicular distance from the ground to the hovering hawk (h) is represented by the height of the triangle.
You are told that the angle of elevation from you to the hawk is 24 degrees and this is the angle between the base and the hypotenuse of the right triangle.
If you remember the acronym: SOHCAHTOA, you will see that you can use the Tangent function because you know the length of the side Adjacent to the angle (500 ft.) and you are looking for the length of the side Opposite the angle (h), so you can write:
Tan%2824%29+=+O%2FA or...
Tan%2824%29+=+h%2F500
Multiply both sides by 500.
500%2ATan%2824%29+=+h Use your calculator to find the tangent.
h+=+222.6143 Round to the nearest foot.
h+=+223feet.