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Ivenika [448]
2 years ago
5

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?
SAT
1 answer:
Mekhanik [1.2K]2 years ago
7 0

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.

<h3>What is right angle triangle property?</h3>

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

\tan\theta=\dfrac{b}{a}

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

H=40^o

From a second position,

I=60\rm\; ft

Farther along this path it is,

b=30^o

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

\tan 40=\dfrac{h}{x}\\h=x\tan 40             ....1

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

\tan 30=\dfrac{h}{x+60}\\h=(x+60)\tan 40               ......2

Compare the equation 1 and 2,

x\tan (40)=(x+60)\tan 30\\0.839x=0.577x+34.64\\0.839x-0.577x=34.64\\x=\dfrac{34.64}{0.262}\\x=132.25\rm\; ft

Put this value in equation 1 as,

h=(132.25)\times \tan40\\h\approx111\rm\;ft

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.

Learn more about the right angle triangle property here;

brainly.com/question/22790996

#SPJ1

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