Expert: Azeem Hussain - 5/5/2009

Question
hi, can you please help me drawing and solving this problem. i tried but i don't think it is the right answer...

The trunk of a leaning tree makes an angle of 12 degree with the vertical. To prevent the tree from falling over, a 35m rope is attached to the top of the tree and is pegged into level ground some distance away.If the tree is 20m from its base to its top, calculate the angle the rope makes with the ground to the nearest degree.

I tried and i got 68 degree...please help me....

Answer
Hi Rabia!

This problem requires you to use basic trigonometry twice.  Begin by drawing your tree tilted at 12 degrees to the vertical.  Solve the height of the vertical.
cos12=v/20
v=(20)cos12

Now draw a new vertical from the tilted tree.  This height is v.  Draw in your rope.  This forms a right triangle with the ground, where the 35 m rope is the hypotenuse.  Set up the equation and solve for angle x
sinx=v/35
sinx=(20)cos12/35
x=33.98

ANSWER: The angle the rope forms with the ground is 33.98 degrees.

Thanks for asking,
Azeem