Question 1205048
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a hawk sitting on a tree branch spots a mouse on the ground 15 feet from the base of the tree. 
the hawk swoops down toward the mouse at an angle of 30 degree. 
what is the distance from the tree branch to the mouse?
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        The solution in the post by @mananth is incorrect.

        I came to bring a correct solution.



<pre>
In this problem, we have a right angle triangle.

Its horizontal leg is  a = 15 feet

The adjacent acute angle is  {{{theta}}} = 30 degrees.


The unknown is the hypotenuse 'c'.


We write  {{{cos(theta)}}} = {{{a/c}}}  and find from it

    c = {{{a/cos(30^o)}}} = {{{15/((sqrt(3)/2))}}} = {{{30/sqrt(3)}}} = {{{10*sqrt(3)}}} = 10*1.732050808 = 17.32 ft  (rounded).


<U>ANSWER</U>.  The distance under the question is  {{{10*sqrt(3)}}} = 17.32 ft  (rounded).
</pre>

Solved correctly.