Aperson 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? (round to the nearest foot)

    Distance between the sailboat and the yacht is 524 feet.

From the figure attached,

Let the distance between sail boat and the yacht (CD) = x feet

Applying tangent rule in ΔABD for angle measuring 42°,

tan(42°) =

             =

tan(42°) =

BD =

BD = 222.12 feet

Apply tangent rule in ΔABC for the angle measuring 25°.

tan(15°) =

BC =

BC = 746.41 feet

Since, BC = BD + CD

746.41 = 222.12 + x

x = 746.41 - 222.12

x = 524.29 feet

x ≈ 524 feet

    Therefore, distance between the sailboat and the yacht is 524 feet.

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524 feet.

Step-by-step explanation:

Given: The height of cliff is 200 feet.

           Angle of depression at sailboat is 42°

           Angle of depression at a yacht is 15°

We will use tangent rule to find distance of sailboat and yacht from cliff´s bottom.

We know, the opposite leg has a height 200 feet.

Formula,

First finding distance of sailboat from bottom of cliff.

⇒

Cross multiplying

we get, Adjacent leg=

∴ Distance of sailboat from cliff´s bottom is 87.33 feet.

Now, finding the distance of yatch from bottom of cliff.

⇒

Cross multiplying

we get, Adjacent leg=

∴ Distance of yatch from cliff´s bottom is 746.5 feet.

Next, finding difference between sailboat and yatch.

Difference=

⇒ Difference=

Hence, the distance between sailboat and yacht is 524 feet.

5104.38 inches

step-by-step explanation: