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(20086) About Me  (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:

x%2F20%22%22=%22%22adjacent%2Fhypotenuse%22%22=%22%22cos%2812%5Eo%29 

x%2F20%22%22=%22%22cos%2812%5Eo%29%2F1

Cross-multiply

x%22%22=%22%2220cos%2812%5Eo%29

Then, using the large right triangle: 

x%2F35%22%22=%22%22opposite%2Fhypotenuse%22%22=%22%22sin%28theta%29

%2820cos%2812%5Eo%29%29%2F35%22%22=%22%22sin%28theta%29

0.5589414861%22%22=%22%22sin%28theta%29

theta%22%22=%22%2233.98262602%5Eo

Rounding to the nearest degree, about 34o

Edwin

Answer by MathTherapy(10858) About Me  (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 matrix%281%2C5%2C+sin+A%2Fa%2C+%22=%22%2C+sin+B%2Fb%2C+%22=%22%2C+sin+C%2Fc%29
In this case, we have: 
                                                                     OR
                                                             
                                                          matrix%281%2C3%2C+35+%2A+sin+%28theta%29%2C+%22=%22%2C+20+%2A+sin+%28102%5Eo%29%29 ------ Cross-multiplying