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Two boats start their journey from the same point A and travel along directions AC and AD, as shown below:
What is the distance, CD, between the boats?

284.3 ft
115.5 ft
230.9 ft
173.2 ft

Two boats start their journey from the same point A and travel along directions AC and AD as shown below What is the distance CD between the boats 2843 ft 1155 class=

Respuesta :

In triangle ABD, [tex]\angle D[/tex] = 30°

Applying trigonometry,

[tex] \boxed {\mathrm{ \tan(30) = \dfrac{ AB}{BD} }}[/tex]

  • [tex] \dfrac{1}{ \sqrt{3} } = \dfrac{100}{BD } [/tex]

  • [tex]BD = 100 \sqrt{3} [/tex]

Now, In triangle ABC, [tex]\angle C[/tex] = 60°

Applying trigonometry,

[tex] \boxed{ \mathrm{ \tan(60) = \frac{AB}{BC} }}[/tex]

  • [tex] \sqrt{3} = \dfrac{100}{BC} [/tex]

  • [tex]BC = \dfrac{100}{ \sqrt{3} } [/tex]

Measure of CD = BD - BC

  • [tex]CD = 100 \sqrt{3} - \dfrac{100}{ \sqrt{3} } [/tex]

  • [tex]CD = \dfrac{300 - 100}{ \sqrt{3} } [/tex]

  • [tex]CD = \dfrac{200}{ \sqrt{3} } [/tex]

  • [tex]CD = 115.47 \: \: ft[/tex]

  • [tex] \boxed {\mathrm{CD \approx115.5 \: \: ft}}[/tex]

_____________________________

[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]

Answer:

B (115.5)

Step-by-step explanation:

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