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? 
<pre>Use the law of sines {{{matrix(1,5, sin A/a, "=", sin B/b, "=", sin C/c)}}}
In this case, we have: {{{matrix(1,3, sin (matrix(1,7, Angle, the, rope, makes, with, the, ground))/matrix(1,3, height, of, tree), "=", sin (matrix(1,6, Angle, tree, makes, with, the, ground))/matrix(1,3, Length, of, rope))}}}
                                                                     OR
                                                             {{{matrix(2,3, sin (theta)/20, "=", sin (90^o + 12^o)/35, sin (theta)/20, "=", sin(102^o)/35)}}}
                                                          {{{matrix(1,3, 35 * sin (theta), "=", 20 * sin (102^o))}}} ------ Cross-multiplying    
                                                             {{{matrix(1,5, sin (theta), "=", (20 * sin (102^o))/35, "=", 0.558941486)}}}
                                                                {{{matrix(1,8, highlight(theta), "=", sin^(- 1)(.558941486), "=", 33.9825, "=", highlight(33.98^o), "(rounded)")}}}</pre>