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valkas [14]
2 years ago
13

A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, t

he angle of depression to the boat is 18°33'. When the boat stops, the angle of depression is 51°33'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.
Mathematics
2 answers:
xxMikexx [17]2 years ago
5 0
If we let
x as the distance traveled by the boat
y as the distance between the boat and the lighthouse.

Then, we have:
tan 18°33' = 200 / (x + y)
and
tan 51°33' = 200 / y

Solving for y in the second equation:
y = 200 / tan 51°33'

Rearranging the first equation and substituting y
x = 200 / tan 18°33' - 200 / tan 55°33'
x = 458.81 ft

Therefore, the boat traveled 458.81 ft before it stopped.
patriot [66]2 years ago
4 0

Answer: 437.21 ft

Step-by-step explanation:

First off, change all minutes to degrees.

18°33’ = 18.55°

51°33’ = 51.55°

When the boat is first spotted:

Tan(x)=opp/adj

Tan(18.55°)=200/x

x=200/tan(18.55)

x=596.01ft

When the boat stops:

Tan(51.55)=200/x

x=158.80ft

Find the difference:

596.01-158.0=437.21

Yay! It’s very simple once you understand the parttern :)

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Answer:

When you divide a positive number (such as 1,000) by a number greater than 1 (such as 5), the answer must be smaller than the number you started with. The answer must be smaller than 1,000. 2,000 is greater than 1,000, so it cannot be correct. The correct quotient is 1,000/5 = 200.

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Answer:

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