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3 years ago

I need some help please

Mathematics

1 answer:

nataly862011 [7]3 years ago

7 0

The side measuring 6.2 is adjacent to the reference angle x. 9 is the measure of the hypotenuse. The trig ratio that relates the side adjacent to the hypotenuse is cosine. We will actually use inverse cosine because what we are looking for is an angle measure. Setting up properly, we have $cos(x)= \frac{6.2}{9}$ . When we do the division we get cos(x) = .68888888 In order to find the angle that has a cosine ratio of .6888888, we will hit the 2nd button on our calculator and then the cos button and we will see this on our display: $cos ^{-1}$ and a parenthesis that is open. Enter that .688888 in and hit enter and you'll get an angle measure of 46.45 or 46.5 rounded. First choice from above.

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The first thing we are going to assume for this case is that the tree and the post are located in the same place.
From that place, both cast a shadow in the same direction.
We then have two similar triangles.
Therefore, we have the following relationship:
$\frac{x}{48} = \frac{5}{8}$
From here, we clear the value of x.
We have then:
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Answer:
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Answer:

Part A

Yes

Part B

He will land at a point 30 meters from Cannon

Step-by-step explanation:

Part A

The given function that represent the path of the Cannon, which is the path of a parabolic arc, is presented as follows;

f(x) = -0.05·(x² - 26·x - 120)

We note that the height, 'h', of the path of a parabola at a horizontal distance, 'x' from the origin is equal to f(x)

Therefore, given that at the ground level, at the start and end of the flight, the f(x) = 0, we can write;

-0.05·(x² - 26·x - 120) = 0

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x = (26 ± √((-26)² - 4 × 1 × (-120)))/(2 × 1)

Which gives;

x = 30 or x = -4

Therefore, he lands at a point 30 meters from the starting point

Therefore, the function gives enough information to tell where he will land

Part B

He lands at the point, x = 30 from the point the cannon was fired.

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