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January 30, 2015

January 30, 2015

Posted by **Lily** on Friday, August 19, 2011 at 2:15am.

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?

- Math -
**Henry**, Friday, August 19, 2011 at 3:33pmFirst 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.

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