What’s the correct answer
2 answers:
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<h2>Right answer: I and II only </h2>
If we already have the formula to find how temperature measured in degrees Fahrenheit, relates to a temperature in degres Celsius:
(1)
We can know the formula to find how temperature measured in degrees Celsius, relates to a temperature in degres Fahrenheit, only by isolating F:
(2)
Having both formulas, let’s begin:
I) If we want to prove that a temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 5/9 degree Celsius:
Beginning with :
This means:
Now we are going to increase 1 degree Farenheit. In other words, we are going to use :
This means:
Calculating the difference between and
:
>>>>This is equal to 5/9 degree Celsius, hence is correct
II) If we want to prove that a temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit:
Beginning with :
This means:
Now we are going to increase 1 degree Celsius. In other words, we are going to use :
This means:
Calculating the difference between and
:
>>>>This is a proof of the statement, hence is also correct.
III) If we want to prove that a temperature increase of 5/9 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius:
Beginning with :
This means:
Now we are going to add :
And use this value in the Celsius formula:
This means:
In other words: An increase in 5/9 degree Fahrenheit is equivalent to a temperature increase of 1.30 degree Celsius, <u>not 1 degree Celsius</u>.
Therefore this statement is incorrect.
The height of the tree, which Pat needs to determine, before cutting it down to be sure that it will not fall on a nearby fence is 111 ft.
<h3>What is right angle triangle property?</h3>In a right angle triangle, the ratio of the opposite side to the base side is equal to the tangent angle between them.
Here, (b) is the opposite side, (a) is the base side.
Pat needs to determine the height of a tree before cutting it down to be sure that it will not fall on a nearby fence.
The angle of elevation of the tree from one position on a flat path from the tree is
From a second position,
Farther along this path it is,
Let the distance between tree and first position is x. Thus, from the trigonometry,
....1
The distance between tree and second position is (x+60) ft. Thus, again from the trigonometry,
......2
Compare the equation 1 and 2,
Put this value in equation 1 as,
Thus, the height of the tree, which Pat needs to determine, before cutting it down to be sure that it will not fall on a nearby fence is 111 ft.
Learn more about the right angle triangle property here;
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