Friday

November 21, 2014

November 21, 2014

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.

**Answer this Question**

**Related Questions**

Math - Please can someone show me the steps to do this problem?? Also, please ...

chemistry - This question I really don't get it. I tried tried tried to figure ...

Math - I came up with no solution for this equation. Could someone please let me...

Math - I have tried to figure out this problem and I just don't seem to ...

math 012 please help explain - can someone please help explain how to do this ...

REVISION - what good websites are there that help with science and maths ...

History - Why was Catherine de Medici disliked? Please don't give me a Google ...

Geometry-Solve for x - ok so I have to solve for x in this problem. and I have ...

Algebra - I've tried and tried and just can't do it. Please help solve this ...

Chemistry - Please help! I have spent hours trying to work these three problems...