SOLUTION: 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

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Question 1205048: 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?
Found 3 solutions by mananth, greenestamps, ikleyn:
Answer by mananth(16949) About Me  (Show Source):
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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?
sin%28theta%29=+opposite+side+%2Fhypotenuse

sin%2830%29=+15%2Fhypotenuse
hypotenuse = 15/ sin(30)''
sin 30 = 1/2

distance from the tree branch to the mouse is 30 ft.

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Answer by greenestamps(13295) About Me  (Show Source):
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Assuming a vertical tree and a flat ground, we have a right triangle.

In that right triangle, the 30 degree angle is formed by the ground and the distance from the hawk to the mouse. So the 15 feet from the mouse to the base of the tree is the long side of the triangle and the unknown distance from the hawk to the mouse is the hypotenuse.
      15                 sqrt(3)
  ---------- = cos(30) = -------
  hypotenuse                2

                  30
  hypotenuse = ------- = 10*sqrt(3) = 17.32 feet to 2 decimal places
               sqrt(3)

ANSWER: about 17.32 feet

Answer by ikleyn(53618) About Me  (Show Source):
You can put this solution on YOUR website!
.
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?
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


        The solution in the post by @mananth is incorrect.
        I came to bring a correct solution. 


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%28theta%29 = a%2Fc  and find from it

    c = a%2Fcos%2830%5Eo%29 = 15%2F%28%28sqrt%283%29%2F2%29%29 = 30%2Fsqrt%283%29 = 10%2Asqrt%283%29 = 10*1.732050808 = 17.32 ft  (rounded).


ANSWER.  The distance under the question is  10%2Asqrt%283%29 = 17.32 ft  (rounded).

Solved correctly.