Respuesta :
Answer:
524.5 feet
Step-by-step explanation:
Given: Height of cliff= 200 ft
Angle of depression at sail boat is 42°
Angle of depression at yacht is 15°
Lets assume distance sailboat from the bottom of cliff is "[tex]d_1[/tex]"
And assume distance yacht from the bottom of cliff is "[tex]d_2[/tex]"
Now using tangent rule to solve it.
we know, [tex]tan\theta = \frac{opposite}{adjacent}[/tex]
Distance sailboat from the bottom of cliff; [tex]tan 42= \frac{200}{d_1}[/tex]
Using trignometry table to know the value of tan 42°
⇒[tex]0.90= \frac{200}{d_1}[/tex]
cross multiplying both side.
⇒ [tex]d_1= \frac{200}{0.90} = 222.22 \approx 222[/tex]
∴ Distance sailboat from the bottom of cliff ([tex]d_1)[/tex]= 222 feet
Distance yatch from the bottom of cliff; [tex]tan 15= \frac{200}{d_2}[/tex]
Using trignometry table to know the value of tan 15°
⇒[tex]0.2679= \frac{200}{d_2}[/tex]
cross multiplying both side.
⇒ [tex]d_2= \frac{200}{0.2679} = 746.54 \approx 746.5[/tex]
∴Distance yacht from the bottom of cliff [tex](d_2)[/tex]= 746.5 feet.
Next, finding the distance between sailboat and yacht.
Distance between sailboat and yacht = [tex]d_2-d_1[/tex]
⇒ Distance between sailboat and yacht= [tex]746.5-222= 524.5\ ft[/tex]
∴ Distance between sailboat and yacht is 524.5 feet.
