Math
posted by Lily on .
Please can someone show me the steps to do this problem?? Also, please don't tell me to just google the solution because I've already tried and have tried to do this problem by myself for hours now...Thank you so much.
You are measuring trees in a forest. Standing on the ground exactly half waybetweentwo trees, you measure the angle the top of each tree makes with the horizon: one angle is 67◦, and the other is 82◦. If one tree is 80 feet taller than the other, how far apart (horizontal distance along the ground) are the two trees?

First we draw a picture that represents
the problem:
1. Draw a hor. line which represents the distance between the 2 trees.
2. Draw a vertical line from the Lt end
of the hor line upward and label it X.
This is the shorter tree.
3. Draw a hyp. from the top of ver line
to center of hor line. Label each half
of hor line "a."
4. Draw a ver. line at the rt end of hor line and label it X+80. This is the taller tree.
5. Draw a hyp from the top of taller tree to center of hor line.
6. The angle between hyp and hor of smaller tree = 67 deg. It is 82 deg for larger tree.
tan67 = X/a,
a = X/tan67.
tan82 = (X+80)/a,
a = (X+80)/tan82.
X/tan67 = (x+80)/tan82,
Cross multiply:
(X+80)tan67 = Xtan82,
2.36X + 188.47 = 7.12X,
7.12x  2.36x = 188.47,
4.76x = 188.47,
X = 39.6 Ft.
X + 80 = 119.6 Ft.
a = X/tan67 = 39.6/tan67 = 16,80 Ft.
d = 2a = 2 * 16.8 = 33.6 Ft. = Distance
between trees. 
google the probelm