Expert: Josh - 5/20/2006

Question
hi, I am stuck on this confusing question and I need help.

As a lumberjack, you attach a 50-foot wire from the top of a leaning pine tree to a stake in the ground, forming a 70 degree angle with the ground. You then measure the distance along the ground from the stake to the center of the tree's base. To determine the length of the tree, what law or theorem should you use?

A. Law of Sines
B. Law of Cosines
C. Pythagorean Theorem
D. Quadratic Formula

Thank you sooooooo much for your help! :)

Answer
Try translating the word problem into a picture.

P
|
|
|
|
G-------------------S

Here, P denotes the top of the pine tree; S the stake; |PG| represents the height of the pine tree (as measured from the ground); |PS| is the length of the wire.

Given: |PS|=50, angle ^GSP=70 degrees.

Assuming that I've got the situation right, to find the length of the tree, we need to work out |PG|. Recall that the sine of angle ^GSP is given by the ratio of the opposite side to the hypotenuse.

i.e., sin(^GSP)=|PG|/|PS|.

Therefore, the tree has length |PG|=|PS|*sin(^GSP).
Putting in the values, |PG|=50*sin(70).

We used the law of sine.