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Expert: - 5/19/2009


Question
QUESTION: a tree 12 meter high is broken by the wind in such a way that its top tuches the ground and makes an angle of 60° with the ground. At what height from the bottom the tree is broken by the wind.

ANSWER: The tree falls in such a way to make a 60° angle with the ground.
That means the angle where the tree is broken is 30².

Using this, it is known that the height of the tree is 1 unit and
the length of the fallen tree is the hypoteneuse of a 30°-60° right triangle, which makes it 2 units.

All together we have (1+2) units = 3 units.

Now to divide 12 ft into 3 units, we need 4 ft / unit.

Since the height it broke at was 1 unit up, that means it faw 4 ft.


---------- FOLLOW-UP ----------

QUESTION: it is giving different result by by taking sin 60° and height h and hypotenuses 12-h

Answer
Oh yeah, now and then I goof up and do one wrong.

The angle is 60° with the ground.
That means the ground side has lenth 1 unit, the hypoteneus has length 2 untis, and the straight up (that's the part left standing) has length √3 units.

This means that (2 + √3)units = 12 meters.

Making the division, this means that 1 unit = 12/(2+√3) meters.

Now since (12 meters)/(2+√3) = 3.2153903 meters, that's 1 unit.

Since the tree that fell has length 2 units, that means that it is
6.4307806 meters.

Since the part that is standing is √3 units, that means that it is
5.5692194 meters.

When these two are added together, 12 meters is gotten.

It would be safe to round them when I'm all done (In fact, I don't know if I needed to carry that many digits, but I like taking them all until through).

Since the height is rounded to 1200 centimeters we could say the new height was 557 cm and the part of the tree that fell was 643 cm.

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