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maks197457 [2]
3 years ago
12

An ant looks up to the top of a tree at an angle of elevation of 40 degrees. If the ant is 30 feet away from the base of the tre

e, what is the height of the tree
Mathematics
1 answer:
hodyreva [135]3 years ago
3 0
Tangent (40) = tree height / 30 feet
tree height  =  tangent (40) * 30 feet
tree height  =  0.8391 * 30
tree height  =  25.173 feet


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\tt Step-by-step~explanation:

To be able to solve this question, we need to know about the Pythagorean theorem: a² + b² = c². A and b represents the two sides that make the right angle, and C represents the hypotenuse, or the longest side, of the triangle.

\tt Step~1:

We know that the hypotenuse is the longest side of the triangle, so that means 9 is c. One side of the triangle is 6, and we have to solve for b. That means 6 is a. We can plug in our values to the formula like this:

\tt a^2+b^2=c^2\\6^2+b+2=9^2\\36+b^2=81

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Now that we have our equation down, we know what we have to do next: subtract 81 from 36 to get b².

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\Large\boxed{\tt Our~final~answer:~b=\sqrt{45} ~(simplified:3\sqrt{5}) }

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<img src="https://tex.z-dn.net/?f=tanx%5E%7B2%7D%20-%5Cfrac%7B1%7D%7B3%7D%20%3D0" id="TexFormula1" title="tanx^{2} -\frac{1}{3}
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Trigonometry expression

These are expression written as a function of sine, cosine and tangent.

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Hence the value of x from the given function is 4.29

Learn more on trig function here: brainly.com/question/24349828

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