Question 6623: The angle of elevation from the top of a tree to a point 30 feet from its base is 25 degrees. Find the height of the tree.
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! What you'll end up having here is a right triangle whose base is 30 feet, and whose horizontal angle is 25° (aka, the angle at the base). You want to find the height of that triangle (which is actually the height of the tree).
Remember your trigonometric ratios for sin x°, cos x°, and tan x°. SOHCAHTOA can help. (Just in case you don't know, sin x° = opp/hyp, cos x° = adj/hyp, and tan x° = opp/adj).
Out of sin, cosine, and tangent, you'll need to choose which of those three is appropriate for the situation. Our problem involves the base of the triangle (which turns out to be the side adjacent (adj) to the angle) and the height of the triangle (which is actually the opposite (opp) side from the angle you're looking at). Out of the three trigonometric ratios, the tangent (tan x°) involves both opposite and adjacent, so we'll use the tangent.
 <---- Start here
 <----- The tangent of 25° is a particular number that your calculator can compute for you, or an approximate value you can look up on a trigonometric table (but who uses that nowadays?)
 feet. The height of the tree must be a bit over 27 feet.
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