SOLUTION: A tree casts a shadow 6 m long when the sun is at an elevation of 70 degrees. A gardener wishes to fell the tree at ground level and needs to cut the trunk into 4 m lengths to cart

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Question 1113075: A tree casts a shadow 6 m long when the sun is at an elevation of 70 degrees. A gardener wishes to fell the tree at ground level and needs to cut the trunk into 4 m lengths to cart it away. How many cuts must he make?
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
y, how tall the tree when standing
r, distance from tip of shadow to top of tree


6%2Fr=cos%2870%29
r%2F6=1%2Fcos%2870%29
r=6%2Fcos%2870%29


y%2Fr=sin%2870%29
y=r%2Asin%2870%29
y=%286%2Fcos%2870%29%29sin%2870%29

y=6%2Asin%2870%29%2Fcos%2870%29

Cut that into 4-meter sections.
%283%2F2%29%28sin%2870%29%2Fcos%2870%29%29--------compute this using calculator.





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recognize that sin%2870%29%2Fcos%2870%29=tan%2870%29.

Answer by MathTherapy(10557) About Me  (Show Source):
You can put this solution on YOUR website!

A tree casts a shadow 6 m long when the sun is at an elevation of 70 degrees. A gardener wishes to fell the tree at ground level and needs to cut the trunk into 4 m lengths to cart it away. How many cuts must he make?
With x being the height of the tree, we have: matrix%281%2C3%2C+tan+%2870%5Eo%29%2C+%22=%22%2C+O%2FA%29 =====> matrix%281%2C3%2C+tan+%2870%5Eo%29%2C+%22=%22%2C+x%2F6%29

Cross-multiplying, and solving for x will give you 16.484865 m.

Divide that by 4 to get the number of INTEGER-cuts. Drop the decimal.