In this question, we're trying to find the inequality that is true.
To find your answer, we can convert the numbers in the absolute value:
|−5| < 4:
5 < 4 <em>false</em>
|−4| < |−5|:
4 < 5 <em>true </em>
|−5| < |4|
5 < 4 <em>false</em>
|−4| < −5
4 < -5 <em>false</em>
The only true inequality here would be |−4| < |−5|, since it works with the inequality sign.
Answer:
|−4| < |−5|
Complementary angles add up to 90 so
angle + 47 = 90
angle = 90 - 47
angle = 43 so A
Answer:
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You did ask for the EXACT value, which no one has posted yet. The exact value is √(2 + √3)/2. To three decimal places, that is .966.
As for how I got that, I started with a 30-60-90 triangle and extended the longer side by the length of the hypotenuse to get a 15-75-90 triangle, then used Pythagoragus. For some reason, though, most students have an easier time using a half-angle formula, so feel free to do it that way.
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OK, sorry, I see Awesome Sauce also gives an exact value. It is also correct, just looks a little different.
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From your comment in Additional Details, it appears you want to use the angle difference relation: cos(π/12) = cos(π/4 - π/6). That works also, but you need to get the formula right, which is:
cos(a - b) = cos a * cos b + sin a * sin b
For cos (45 - 30), this gives cos 45 * cos 30 + sin 45 * sin 30 = √2/2 * √3/2 + √2/2 * 1/2 = √2/4(√3 + 1). This is yet another expression for the same exact value.
If you divide 90 by 6 you get 15. This means the answer is 2.
