Find the value of x. If necessary, write your answer in simplest radical form. x=?
1 answer:
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Answer:
the angle between their paths is <em>100.8°</em>
Step-by-step explanation:
From the given information, you can construct a triangle, just like the one in the figure.
We will use the <em>Cosine Rule</em> which is:
c² = b² + a² - 2 b c cos(θ)
where
- c = 16 miles
- b = 8 miles
- a = 12 miles
Therefore,
2 b c cos(θ) = b² + a² - c²
cos(θ) = (b² + a² - c²) / 2 b c
θ = cos⁻¹( (b² + a² - c²) / (2 b c) )
θ = cos⁻¹( (8² + 12² - 16²) / 2(8)(16) )
<em>θ = 100.8°</em>
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Therefore, the angle between their paths is <em>100.8°</em>
Answer:
Step-by-step explanation:
1. Make sure all your denominators are the same, you can do this by multiplying them all by 3 or 7, 2 and 1/3 would become 2 7/21, 3/7 would become 9/21, 2 and 1/3, would become 2 and 7/21, and so on and so forth, leaving us with
2+
/ 2
* 1
2. Now, I would go and solve each side of the equation because we divide them, we can add 2 and
together to get 2
, because 7 + 9 = 16
2 / 2
* 1
3. We can do the same thing to the other side, by multiplying the two of them. I'm going to convert both of them to just fractions, 2 becomes
and 1
becomes
*
Now we can reduce them, and for our first fraction divide the top and bottom by 7, giving us and the second one by 3, which gives us
*
now we cross divide, where we replace the 7's with ones because they're right across from each other to get
and
, or just 10.
* 10 =
4. So now we can do a similar thing with the first half of our equation and convert it into a fraction and not a mixed number.
/
Now we multiply divide them, and the easiest way I learned how to do this was by keep the first fraction in its place, and flipping the denominator and numerator of the second, and multiplying them.
so *
which if we multiply both sides, you get
I'll save you some times and simplify it for you, the greatest common factor is 6 so we divide the top and bottom by 6 to get