Answered

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Over 2 miles (horizontal), a road rises 300 feet (vertical). What is the angle of elevation?

Note: 1 mile is 5,280 feet.

Select one:

a.
3.25°


b.
1.6°


c.
1.75°


d.
86.7°

Sagot :

Kawaiimikuidn

Answer:

b. 1.6°

Step-by-step explanation:

To find the angle of elevation, we can use the tangent function, which is the ratio of the opposite side (vertical rise) to the adjacent side (horizontal distance).

First, convert the horizontal distance from miles to feet:

[tex][ 2 \text{ miles} = 2 \times 5280 \text{ feet} = 10,560 \text{ feet} ][/tex]

Next, use the tangent function:

[tex][ \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{300 \text{ feet}}{10,560 \text{ feet}} ][/tex]

[tex]Now, calculate \: the \: angle (\theta):[/tex]

[tex][ \theta = \tan^{-1}\left(\frac{300}{10,560}\right) ][/tex]

Using a calculator to find the arctan (inverse tangent):

[tex][ \theta = \tan^{-1}(0.0284) \approx 1.63^\circ ][/tex]

The closest answer to this calculation is: b. 1.6°

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