"A length of rope is stretched between the top edge of a building and a stake in the ground. The head of the stake is at ground level. The rope also touches a tree that is growing halfway between the stake and the building. If the the building is 36 feet tall, how tall is the tree?" How do I solve this?

Question

anonymous · Answer

Here is the picture for the question.

anonymous · Answer

ok this tough one just use a tape to measure

anonymous · Answer

i thinkthe tree is 18 feet tall

anonymous · Answer

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anonymous · Answer

$$\tan^{-1} (h/L) = \tan^{-1} (t/(L/2))$$ where h = 36 and t = height of tree

If you solve for t here, you get t = h/2

anonymous · Answer

does that mean i am close diracdelta?

anonymous · Answer

yup :)

anonymous · Answer

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jhannybean · Answer

@Kittens4Mittens you're making it to complicated, I think.

anonymous · Answer

naa brew

jhannybean · Answer

@diracdelta 's logic is correct, he/she need to explain how they found using $\tan^{-1}(\theta)$ would work.

anonymous · Answer

Thank you! @diracdelta and @Kittens4Mittens! The formula you provided will help me for the next several problems. Thank you!

anonymous · Answer

diracdelta how you figure the formula out?

anonymous · Answer

@Jhannybean is right, I should have mentioned that my reasoning was very simple.  Basically if you look at your drawing, the easiest thing that the 2 triangles have in common is the angle.  Remember the inverse of any trig function always spits out an angle :)

jhannybean · Answer

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