Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence. the angle of elevation of the tree from one position on a flat path from the tree is and from a second position farther along this path it is what is the height of the​ tree?
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The height of the​ tree, which Pat needs to determine, before cutting it down to be sure that it will not fall on a nearby fence is 111 ft.

### What is right angle triangle property?

In a right angle triangle, the ratio of the opposite side to the base side is equal to the tangent angle between them.

Here, (b) is the opposite side, (a) is the base side.

Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence.

The angle of elevation of the tree from one position on a flat path from the tree is

From a second position,

Farther along this path it is,

Let the distance between tree and first position is x. Thus, from the trigonometry,

....1

The distance between tree and second position is (x+60) ft. Thus, again from the trigonometry,

......2

Compare the equation 1 and 2,

Put this value in equation 1 as,

Thus, the height of the​ tree, which Pat needs to determine, before cutting it down to be sure that it will not fall on a nearby fence is 111 ft.
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