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September 21, 2014

September 21, 2014

Posted by **Lily** on Friday, August 19, 2011 at 2:20am.

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 -
**Reiny**, Friday, August 19, 2011 at 7:51ammake a diagram, showing the two trees at A and B, labeled h for the height of the shorter, and h+80 for the height of the taller.

let P be the midpoint of AB , where AP = BP

Then the angle at P for the taller tree is 82° , and the angle at P for the smaller tree is 67°

then h/AP = tan67° and (h+80)/BP = tan82°

AP = h/tan67 and BP = (h+80)/tan82

but AP and BP are equal, so

h/tan67 = (h+80)/tan82

htan82 = htan67 + 80tan67

htan82 - htan67 = 80tan67

h(tan82-tan67) = 80tan67

h = 80tan67/(tan82-tan67) = .....

You do the button - pushing

once you have h, sub it back into the little equation for AP

(I got AP= 16.8)

- Math -
**Anonymous**, Saturday, June 21, 2014 at 4:03pmWhat does tan67 equal?

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