The REAL hardest math question ever

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1

<p>OK, I posted the wrong link in the other thread. so this is the REAL question I couldn't get.</p>

<p><a href="http://i475.photobucket.com/albums/rr116/watex/pic-2.png%5B/url%5D"&gt;http://i475.photobucket.com/albums/rr116/watex/pic-2.png&lt;/a> </p>

<p>No idea. The answer was E. I just thought it had to be the largest angle because it's the largest side.</p>

2

<p>It has to be greater than 90 because it would be equal to 90 in 3-4-5 right triangle and by making the hypotenuse longer you increase the degree of angle Q.</p>

3

<p>The triangle is obtuse. You can kind of draw this out in front of you. Start with point P, then draw a line segment going straight down to Q. From here, you could either draw a line to R from Q that is angled upward, horizontal, or downward. The only possible choice is downward, because, as the above poster mentioned, a 3,4,5 triangle would be right. A 3,4,<5 triangle would be acute. This is a 3,4,6 (>5), so it has to be obtuse. Therefore, angle PQR must be greater than 90, hence E.</p>

<p>At least tell me you drew the triangle out. If you didn’t draw it out, then that is a bad strategy. Always draw out these simple shapes. Generally, the answer becomes self-evident and, even if not, you don’t have to juggle numbers, mental images, and questions all in one.</p>

4

<p>4^2 + 3^2 < 6^2 so by the converse of the Pythagorean theorem, the triangle is obtuse. The obtuse angle must be opposite the largest side (6), so x is obtuse and hence > 90.</p>

5

<p>This does not compare to that radius question from the SAT!</p>

6

<p>senior- how am I supposed to measure out exactly 4,5, and 6 units? I dont have a ruler on the test or any tool precise enough to do that</p>

<p>anh- wat radius question?</p>

<p>jamesford- so if I do the Pyth. theorm and the hypotnuse side is greater than the other 2, the triangle is obt. if it is smaller, it is acute</p>

7

<p>
[QUOTE=Wikipedia]

A corollary of the Pythagorean theorem’s converse is a simple means of determining whether a triangle is right, obtuse, or acute, as follows. Where c is chosen to be the longest of the three sides:</p>

<pre><code>* If a^2 + b^2 = c^2, then the triangle is right.

  • If a^2 + b^2 > c^2, then the triangle is acute.
  • If a^2 + b^2 < c^2, then the triangle is obtuse.
    </code></pre>

<p>

[/quote]
</p>

<p>There you are</p>

8

<p>You can just draw it with rough estimates. I drew it by hand on my computer screen.</p>

9

<p>As the others have said its obvious it has to be greater than 90 because of Pythagorean theorem, but if you were really un-sure you could have used the law of cosines.</p>

10

<p>Instead of using the pythagorean theorem to approximate the angle, you can easily find the largest angle using the law of cosines. Make the side that is 6 c, and by c^2=a^2+b^2-2ab(cos(c)) you get 36=(16+9)-(2<em>4</em>3*cos(c)) which simplifies to 11=-24cos(c). divide by -24 and take the inverse cosine of your answer and you get the angle is approximately 117 degrees, making the answer choice E.</p>

11

<p>That wasnt hard.</p>

<p>remember the 3-4-5 right triangle, since 5 corresponds to 90 , and x corresponds with 6, x has to be greater than 90.</p>

12

<p>Another bumped old thread…</p>

13

<p>Shouldn’t the “REAL hardest math question ever” be something like: why can every even number greater than two be written as the sum of two primes?</p>

<p>( and this would be a grid-in :slight_smile: )</p>