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Kazeer [188]
2 years ago
5

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 16°23'. When the boat stops, the angle of depression is 49°29' . 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
1 answer:
matrenka [14]2 years ago
3 0

Answer:

509.35 feet

Step-by-step explanation:

16°23' means 16 degrees and 23 minutes.  A minute is 1/60 of a degree.

16°23' = 16 + (23/60) = 16.383°

Similarly:

49°29' = 49 + (29/60) = 49.483°

When the boat is first noticed:

tan(16.383°) = 200 / a

a = 200 / tan(16.383°)

a = 680.27

When the boat stops:

tan(49.483°) = 200 / b

b = 200 / tan(49.483°)

b = 170.92

So the difference is:

a − b = 680.27 − 170.92 = 509.35

The boat traveled 509.35 feet from the time it was first noticed to the time it stopped.

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Answer:

|t| =|-0.96|=0.96< 2.718

since calculated' t' value is less than tabulated value 't'.

we accept null hypothesis at 1 % level of significance.

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Step-by-step explanation:

<u>Step:-(1)</u>

Given the sample size n = 12

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mean of the sample(x⁻) = $0.95

Standard deviation of sample (S) = $0.18

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<u>Null hypothesis:</u>-H₀:'μ' =  $1.00.

<u>Alternative hypothesis</u>: H₁:'μ' ≠  $1.00.

<u>level of significance ∝ = 0.01</u>

<u>Step2:-</u>

<u>The test statistic </u>

t = \frac{x^{-}-u_{0}  }{\frac{S}{\sqrt{n} } }

t = \frac{0.95-1 }{\frac{0.18}{\sqrt{12} } }

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since calculated' t' value is less than tabulated value 't'.

<u>conclusion</u>:-

<u>we accept null hypothesis at 1 % level of significance.</u>

<u>The data support the claim that the mean cost of a daily news paper is  $1.00</u>

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Answer:

The answer is B. Hope this helps!

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