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
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-> 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
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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?
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
