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Arisa [49]
3 years ago
10

Starting at point​ A, a ship sails 18.9 km on a bearing of 190 degrees and ​then turns and sails 47.2km on a bearing of 318 degr

ees. Find the distance of the ship from point A. (Use trigonometry)

Mathematics
1 answer:
lara31 [8.8K]3 years ago
4 0

Answer:

Approximately 38.56 kilometers

Step-by-step explanation:

So, from the picture, we want to find <em>x</em>.

To do this, we can use the Law of Cosines. We simply need to find the angle between the two sides and then plug them into the Law of Cosines. First, the Law of Cosines is:

c^2=a^2+b^2-2ab\cos(C)\\

The <em>c </em>in this equation is our <em>x, </em>and the <em>C</em> is the angle we need to find.

From the picture, you can see that angle <em>C </em>is the sum of the red and blue angles.

From a bearing of 190 degrees, we can determine that the red angle measures 10 degrees. Then by alternate interior angles, the other red angle must also measure 10 degrees.

From a bearing of 318 degrees, the remaining 48 degrees is outside the triangle. However, we have a complementary angle, so we can find the angle inside the triangle by subtracting in into 90. Therefore, the blue angle inside is 90-48=42 degrees.

Therefore, angle <em>C </em> is 42+10 which equals 52 degrees. Now we can plug this into our formula:

x^2=a^2+b^2-2ab\cos(C)\\\\x^2=(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)\\x=\sqrt{(18.9)^2+(47.2)^2-2(18.9)(47.2)\cos(52)}\\\text{Use a Calculator}\\x\approx38.5566 \text{ km}

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damaskus [11]

Explanation:

Each row in Pascal's triangle is a listing of the values of nCk = n!/(k!(n-k)!) for some fixed n and k in the range 0 to n. nCk is <em>the number of combinations of n things taken k at a time</em>.

If you consider what happens when you multiply out the product (a +b)^n, you can see where the coefficients nCk come from. For example, consider the cube ...

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The highest-degree "a" term will be a^3, the result of multiplying together the first terms of each of the binomials.

The term a^b will have a coefficient that reflects the sum of all the ways you can get a^b by multiplying different combinations of the terms. Here they are ...

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For this cubic, the third term of the expansion is the sum of the ways you can get ab^2. It is essentially what is shown above, but with "a" and "b" swapped. Hence, there are 3 combinations, and the total is 3ab^2.

Of course, there is only one way to get b^3.

So the expansion of the cube (a+b)^3 is ...

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In short, the values in Pascal's triangle are the values of the number of combinations of n things taken k at a time. The coefficients of a binomial expansion are also the number of combinations of n things taken k at a time. Each term of the expansion of (a+b)^n is of the form (nCk)·a^(n-k)·b^k for k =0 to n.

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When the choice is not relevant, we have:

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