2.8 Summary Questions

1. Determine the total heights of the trees illustrated below. Pay attention to the horizontal distances and slope scale used for each.

at a horizontal distance of 50 ft, reading to top is +137%; reading to stump is -11%
at a horizontal distance of 100 ft, reading to top is +97%; reading to stump is -61%
at a horizontal distance of 120 ft, reading to top is +107%; reading to stump is -12%
at a horizontal distance of 66 ft, reading to top is +101 Tslope; reading to stump is -8 Tslope
at a horizontal distance of 33 ft, reading to top is +90 Tslope; reading to stump is -10 Tslope

2. How should the total height of this flat-topped tree be determined?

graphic of a tree with a broken top - top looks flat

 

3. Calculate the height of the leaning tree.

a leaning tree. at a horizontal distance of 66 ft, reading to top is +48 Tslope; reading to the top's fall line is -8 Tslope. Horizontal distance from stump to fall line is 54 ft.

 

 

Answers to Summary Questions

1. A. \displaystyle rise=\frac{{\left( {run} \right)}}{{100}}(%slope)

\displaystyle rise=\frac{{\left( {50} \right)}}{{100}}(137+11)

rise (height)= 74 feet

 

I.B. \displaystyle rise=\frac{{\left( {100} \right)}}{{100}}(97+16)

= 113 feet

 

I.C. \displaystyle rise=\frac{{\left( {120} \right)}}{{100}}(107+12)

= 143 feet

 

I.D. \displaystyle rise=\frac{{\left( {run} \right)}}{{66}}(Tslope)

\displaystyle rise=\frac{{\left( {66} \right)}}{{66}}(101+8)

rise (height) =  109 feet

 

I.E. \displaystyle rise=\frac{{\left( {33} \right)}}{{66}}(90+10)

=  50 feet

 

2. The top of the tree will have to be reconstructed because of the broken top. This can be done by using a neighboring tree similar in size and taper as a reference.

 

 

3. a. The rise of the fall line from  the top of the tree to the ground = \displaystyle rise=\frac{{\left( {run} \right)}}{{66}}(Tslope)

\displaystyle rise=\frac{{\left( {run} \right)}}{{66}}(48+8)

=  56 feet

b.  The horizontal distance from the base of the tree to the fall line is 54 feet.  Thus you have two sides of the right triangle.

Using the Pythagorean theorem to determine the tree length (hypotenuse):

a2 + b2 = c2      where:

562 + 542 = c2

6052 = c2       

\sqrt{{6052}}= 78 feet

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2.8 Summary Questions by Joan DeYoung is licensed under a Creative Commons Attribution 4.0 International License, except where otherwise noted.