The angle of elevation from the tip of the shadow to the top of the tree is 36°. What is the distance from the top of the tree to the tip of the shadow?

1 Answer
EZ as pi
Jul 3, 2016

distance = # "length of shadow"/(cos36°)#

Explanation:

The only actual value we have is the angle of elevation (apart from the assumed 90° angle at the base of the tree.)

However. we can call the length of the shadow #x#, as this will be a measurable distance. We are asked for the length of the hypotenuse, but we can only give it "in terms of the length of the shadow" and not as a number answer.

The shadow is the side adjacent to the angle of #36°# , and the length we are asked to find is the hypotenuse. Therefore the trig ratio we are working with is Cos. #(a/h)#

#x/"hypotenuse" = Cos 36°#

However, it would be easier to have the reciprocal.

#"hypotenuse"/x = 1/(cos36°)#

Distance to top of tree(hypotenuse) =# "length of shadow(x)"/(cos36°)#

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