SOLUTION: Bubba and Madge are lying on the grass 100 yards apart. Ideally, they would be making googly eyes at one another, but unfortunately a pine tree stands alone somewhere between the

Question 719674: Bubba and Madge are lying on the grass 100 yards apart. Ideally, they would be making googly eyes at one another, but unfortunately a pine tree stands alone somewhere between them. Madge notices that there is a 17 degree angle of elevation to the top of the tree � Bubba discovers there is a 12 degree angle of elevation to the tree�s top. To the nearest inch, how tall is the tree?

Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
For simplicity of calculation, let Bubba's angle = B and Madge's angle = M
Let x = the distance along the ground from Madge to the tree
Then 100 - x = the distance along the ground from Bubba to the tree
Let h = the height of the tree
tan(M) = h/x -> x = h/tan(M)
tan(B) = h/(100-x) -> tan(B) = h/(100-(h/tan(M))
Simplify and solve for h:
tan(B)(100 - h/tan(M)) = h
h = 100tan(B)/(1+tan(B)/tan(M))
Divide top and bottom by tan(B):
h = 100/(1/tan(B) + 1/tan(M))
Putting in the numbers gives h = 12.5384 yds
0.5384 yds = 19.38 inch
So to the nearest inch the tree is 12 yds 19 inch
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