Question

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?

Answer 1

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°)`