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MA_775_DIABLO [31]
3 years ago
11

At a point on the ground 46 feet from the foot of a tree, the angle of elevation of the top of the tree is 68 degrees. What is t

he height of the tree to the nearest foot?
Mathematics
1 answer:
Mandarinka [93]3 years ago
6 0

Answer:

114 ft

Step-by-step explanation:

Imagine or construct a right triangle with the 46 ft leg lying on the ground.  This is the "adjacent side" of the triangle; it lies immediately adjacent to the 68 degree angle.  The side opposite this angle is h, the height of the tree.

The tangent function includes angle, opp side and adj side:

tan 68 degrees = opp / adj = h / (46 ft), and so:

(46 ft)*tan (68 degrees) = opp = h

Then the height of the tree is h = (46 ft)(2.47) = 114 ft

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3 years ago
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SashulF [63]

Answer:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

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Step-by-step explanation:

For this case first we need to calculate the dot product of the vectors, and after this if the dot product is not equal to 0 we can calculate the angle between the two vectors in order to see if there are parallel or not.

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The dot product on this case is:

a b= (1)*(4) + (2)*(0)+ (-2)*(-3)=10

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Now we can calculate the magnitude of each vector like this:

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And finally we can calculate the angle between the vectors like this:

cos \theta = \frac{ab}{|a| |b|}

And the angle is given by:

\theta = cos^{-1} (\frac{ab}{|a| |b|})

If we replace we got:

\theta = cos^{-1} (\frac{10}{\sqrt{9} \sqrt{25}})=cos^{-1} (\frac{10}{15}) = cos^{-1} (\frac{2}{3}) = 48.190

Since the angle between the two vectors is not 180 or 0 degrees we can conclude that are not parallel

And the anfle is approximately \theta \approx 48

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Answer:

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