Point E is located at coordinates (-7, -5). Point F is located at the coordinates (-2, 7). What is the length of EF?
2 answers:
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Answer:
- 14π/9; 108°; -√2/2; √2/2
Step-by-step explanation:
To convert from degrees to radians, use the unit multiplier
In equation form that will look like this:
- 280° ×
Cross canceling out the degrees gives you only radians left, and simplifying the fraction to its simplest form we have
The second question uses the same unit multiplier, but this time the degrees are in the numerator since we want to cancel out the radians. That equation looks like this:
×
Simplifying all of that and canceling out the radians gives you 108°.
The third one requires the reference angle of .
If you use the same method as above, we find that that angle in degrees is 135°. That angle is in QII and has a reference angle of 45 degrees. The Pythagorean triple for a 45-45-90 is (1, 1, √2). But the first "1" there is negative because x is negative in QII. So the cosine of this angle, side adjacent over hypotenuse, is
which rationalizes to
The sin of that angle is the side opposite the reference angle, 1, over the hypotenuse of the square root of 2 is, rationalized,
And you're done!!!