To support a tree damaged in a storm, a 12-foot wire is secured from the ground to the tree at a point 10 feet off the ground. the tree meets the ground at a right angle. at approximately what angle does the wire meet the ground? 33.6° 39.8° 50.2° 56.4°

This situation represents a right triangle.  The hypotenuse is the length of the wire which is 12.  The height of the wire off the ground is the vertical leg of the triangle which is 10.  The angle we are looking for is the other base angle (not the right angle, the one next to it).  The side measuring 10 is the side opposite the angle in question, and we also have the hypotenuse, so the trig ratio that relates the side opposite to the hypotenuse is sin.  Set it up according to the ratio:  sin of the angle = side opposite over hypotenuse.  .  We can simplify that ratio if we want to (although we are not required to to find the correct angle measure).  .  Plug that into your calculator in degree mode using the 2nd button and then the sin button to find the missing angle value.  Doing this gives you that the angle measures 56.44 or 56.4°, last choice above.

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