Question

During a strong wind, the top of a tree cracks and bends over, touching the ground as if the trunk were hinged. The tip of the tree touches the ground 20 feet 6 inches from the base of the tree and forms a 38° angle with the ground. What was the tree's original height?

Answer 1

http://www.twiddla.com/527982

Answer 2

i solved it but i am not sure if my answer is right

Answer 3

does the tree and the ground form a 90 degree angle?

Answer 4

yes

Answer 5

Ok, so this forms a right angled triangle. The original height of the tree is the side opposite the angle plus the hypotenuse. So:\[\tan 38=\frac{opp}{20.5}\implies opp=20.5\tan 38\approx16.0\]\[Hyp^2\approx20.5^2+16^2\approx676.8 \implies Hyp \approx \sqrt{676.8}\approx26ft\]N.B you can solve this using other trigonometric ratios.

Answer 6

normally trees aren't perfectly edged
but it should give an approximate height if we do assume the angle is 90 degrees there
it is close enough i think
i got 192.196 inches what did you get hikari?

Answer 7

why 20.5 not 20.6?

Answer 8

Because 6 inches is half a foot.

Answer 9

oh i found the height of just the part that wasn't knocked over by the wind
i need to find the hyp. and add the hyp to 192.196 inches to get the full length of the tree

Answer 10

i got for tan was 16.09 and cos is 26.01 then i add it then got 42.1

Answer 11

504.374 inches

Answer 12

504.374inches=42.03 feet

Answer 13

gj our numbers are pretty close

Answer 14

does i did right or not

Answer 15

Yes, you too, got same thing.

Answer 16

Hmm, where did I go wrong then?

Answer 17

bendt you just didn't add the hyp to the rest of the tree to get the whole tree

Answer 18

Oh yeah, duh. I even wrote that you need to do that :P

Answer 19

lol

Answer 20

he i just posted another problem

Answer 21

http://openstudy.com/groups/mathematics/updates/4de813d24c0e8b0bcc43bbd8