SOLUTION: The trunk of a leaning tree makes an angle of 12 degrees with the vertical. To prevent the tree form falling over a 35 m rope is attached to the top of the tree and pegged into th

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Question 1195054: The trunk of a leaning tree makes an angle of 12 degrees with the vertical. To prevent the tree form falling
over a 35 m rope is attached to the top of the tree and pegged into the ground some distance away (assume
the ground is level). If the tree is 20 m tall what angle does the rope make with the ground?
Found 2 solutions by Edwin McCravy, MathTherapy:
Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!



First we find x, the distance from the top of the tree to the ground:

Using the smaller right triangle on the left:

 



Cross-multiply



Then, using the large right triangle: 









Rounding to the nearest degree, about 34o

Edwin
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
The trunk of a leaning tree makes an angle of 12 degrees with the vertical. To prevent the tree form falling
over a 35 m rope is attached to the top of the tree and pegged into the ground some distance away (assume
the ground is level). If the tree is 20 m tall what angle does the rope make with the ground? 
Use the law of sines 
In this case, we have: 
                                                                     OR
                                                             
                                                           ------ Cross-multiplying

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