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Ne4ueva [31]
3 years ago
12

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°18'. When the boat stops, the angle of depression is 48°51'. 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:
7nadin3 [17]3 years ago
4 0

To solve this problem, we can use the tan function to find for the distances covered.

tan θ = o / a

Where,

θ = angle = 90° - angle of depression

o = side opposite to the angle = distance of boat from lighthouse

a = side adjacent to the angle = height of lighthouse = 200 ft

When the angle of depression is 16°18', the initial distance from the lighthouse is:

o = 200 tan (90° - 16°18')

o = 683.95 ft

When the angle of depression is 48°51', the final distance from the lighthouse is:

o = 200 tan (90° - 48°51')

o = 174.78 ft

 

Therefore the total distance the boat travelled is:

d = 683.95 ft - 174.78 ft

<span>d = 509.17 ft</span>

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3 years ago
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oksano4ka [1.4K]

Answer:

Mean : 95

Median : 85

Mode : 90

Part B : Impossible

Step-by-step explanation:

We can make an equation to find the mean using the first 5 history test scores.

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So a 95 would be needed to have a mean of 85.

Next, the median.

First, we sort the first 5 history scores from least to greatest.

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Since, 80 is the middle value, it will be used in the calculation of the median.

We can make an equation with this.

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Thirdly, the mode.

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Finally, Part B.

We can use the equation we had for the first mean calculation but change 85 to 90.

90=\frac{80+75+90+75+95+n}{6} \\ \\ 90=\frac{415+n}{6} \\ \\ 540=415+n \\ \\ n=125

So Maliah would need a score of 125 to make her mean score 90, but since the range is only from 0-100, it is impossible.

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He would earn <span>$40.95 in that amount of time


</span>
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