Mathematics, 11.01.2020 09:31 therealpr1metime45

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)

Answers: 2

Show answers

Answers

Answer from: MarMarMar07

Distance between the sailboat and the yacht is 524 feet.

From the figure attached,

A person is standing at the height above the body of water = 200 feetAngle of depression of the sailboat (at point D) = 42°Angle of depression of a yacht (at point C) = 15°

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

Applying tangent rule in ΔABD for angle measuring 42°,

tan(42°) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

= $\frac{AB}{BD}$

tan(42°) = $\frac{200}{BD}$

BD = $\frac{200}{\text{tan}(42^\circ)}$

BD = 222.12 feet

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

tan(15°) = $\frac{AB}{BC}$

BC = $\frac{200}{\text{tan}(15^\circ)}$

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.

Learn more,

link

Answer from: iamsecond235p318rq

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, $tan \theta = \frac{Opposite\ leg}{adjacent\ leg}$

First finding distance of sailboat from bottom of cliff.

$tan 42= \frac{200}{adjacent\ leg}$

⇒ $0.90= \frac{200}{adjacent\ leg}$

Cross multiplying

we get, Adjacent leg= $\frac{200}{0.90} = 222.22\ feet$

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

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

$tan 15= \frac{200}{adjacent\ leg}$

⇒ $0.2679=\frac{200}{adjacent\ leg}$

Cross multiplying

we get, Adjacent leg= $\frac{200}{0.2679}= 746.5\ feet$

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

Next, finding difference between sailboat and yatch.

Difference= $Yacht\ distance - sailboat\ distance$

⇒ Difference= $746.5 \ feet - 222.22\ feet= 524.32 \approx 524\ feet.$

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

Aperson is standing on a cliff that is 200ft above a body of water. the person looks down at an angl

Answer from: Quest

answer: since the question is talking about growth you have to use the growth formula which is inital amount (1 + growth)^time

step-by-step explanation:

the intial amount is 1200, the growth is 4.8, and the time is 7. plug those numbers into the equation, also i think you have to change 4.8 into a percent. but, i have forgotton how to do that. if this is a online class go on to the lesson.

Answer from: Quest

1) is right

step-by-step explanation:

Can someone helm me with this problem plz and show work

Another question on Mathematics

Mathematics, 21.06.2019 13:30

Is the orthocenter of a triangle on the inside ?

Answers: 2

Answer

Mathematics, 21.06.2019 13:50

What are the vertical asymptotes of the function f(x) =5x+5/x2 + x-2

Answers: 1

Answer

Mathematics, 21.06.2019 14:30

The contents of 3838 cans of coke have a mean of x¯¯¯=12.15x¯=12.15. assume the contents of cans of coke have a normal distribution with standard deviation of σ=0.12.σ=0.12. find the value of the test statistic zz for the claim that the population mean is μ=12.μ=12.

Answers: 1

Answer

Mathematics, 21.06.2019 18:00

On saturday a souvenir shop had 125 customers.sixty four percent of the costumers paid with a credit card. how many costumers paid with cash?

Answers: 1

Answer

You know the right answer?

Aperson is standing on a cliff that is 200ft above a body of water. the person looks down at an angl...

Questions