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a person standing near the top of the Eiffel tower(approximately 300.6 meters) notices a car wreck some distance from the tower. If the angle of depression from the person's eyes to the wreck is 32°, approximately how far away is the accident from the base of the tower? ​

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Dead3ill

Answer:

481.06

Step-by-step explanation:

Let's visualise this case in a right angled triangle.

Height = 300.6 m

Angle of depression = Angle of elevation = 32°

So,

[tex] \sin(32) = \frac{300.6}{hypotenuse} [/tex]

[tex] = > 0.5299192642 = \frac{300.6}{hypotenuse} [/tex]

[tex] = > hypotenuse = \frac{300.6} {0.5299192642 } [/tex]

[tex] = 567.2562224244 m[/tex]

Hypotenuse = Line of sight = 567.25 m

Also,

[tex] \cos(32) = \frac{base}{567.2562224244} [/tex]

[tex] = > 0.8480480962 = \frac{base}{567.2562224244} [/tex]

[tex] = > base = 0.8480480962 \times 567.2562224244 = 481.0605594599[/tex]

Hence Base = Distance between the spot of accident & the base of the tower = 481.06 m

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