Question

A person is standing on a cliff that is 200ft above a body of water. The person looks down at an angle of depression of 42o at a sailboat. Then the person looks at a yacht that is further out at an angle of depression of 15o. What is the distance (in feet) between the sailboat and the yacht?

Answer 1

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 "$d_1$"

And assume distance yacht from the bottom of cliff is "$d_2$"

Now using tangent rule to solve it.

we know, $tan\theta = \frac{opposite}{adjacent}$

Distance sailboat from the bottom of cliff; $tan 42= \frac{200}{d_1}$

Using trignometry table to know the value of tan 42°

⇒$0.90= \frac{200}{d_1}$

cross multiplying both side.

⇒ $d_1= \frac{200}{0.90} = 222.22 \approx 222$

∴ Distance sailboat from the bottom of cliff ($d_1)$= 222 feet

Distance yatch from the bottom of cliff; $tan 15= \frac{200}{d_2}$

Using trignometry table to know the value of tan 15°

⇒$0.2679= \frac{200}{d_2}$

cross multiplying both side.

⇒ $d_2= \frac{200}{0.2679} = 746.54 \approx 746.5$

∴Distance yacht from the bottom of cliff $(d_2)$= 746.5 feet.

Next, finding the distance between sailboat and yacht.

Distance between sailboat and yacht = $d_2-d_1$

⇒ Distance between sailboat and yacht= $746.5-222= 524.5\ ft$

∴ Distance between sailboat and yacht is 524.5 feet.