Step-by-step explanation:
hi I have answered ur question
To approximate the length of a marsh, a surveyor walks x=420 meters from point A to point B,then turns 75 degrees and walks 220
1 answer:
Applying the law of cosine, b² = a² + c² - 2ac(cos B), the length of AC of the marsh, to one decimal place, is: 522.1 meters
<h3>What is the Law of Cosine?</h3>The Law of Cosine is given as, b² = a² + c² - 2ac(cos B).
From the diagram given, we have the following:
- B = 180 - 75 = 105°
- b = AC (length of the marsh)
- a = 220 m
- c = 420 m
Plug in the values into the law of cosine formula:
b² = 220² + 420² - 2(220)(420)(cos 105)
b² = 272,629.8
b = √272,629.8
b = 522.1 meters. (Length of AC of the marsh)
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Answer:
i) A. 180º rotation about the origin, ii) .
Step-by-step explanation:
i) In this case, we understand that vertex changed to
after doing an operation. At first we must calculate the distance of each point regarding origin by Pythagorean Theorem:
Point P:
If we know that ,
,
and
, the distance
is:
Point P':
If we know that ,
,
and
, the distance
is:
As , origin is the center of rotation.
Besides, is a multiple of
, that is:
1) Given
2)
3) Scalar multiplication of a vector/Result.
The value of the scalar proves that P experimented a 180º rotation about the origin. Hence, the correct answer is A.
ii) If and the same operation described in item i) is used, then, the location of
is:
Which corresponds to option C.