<p>In Triangle PQR, PQ = 4 , QR = 3, PR = 6, and the measure of angle PQR is x degrees. Which of the following must be true about x ?</p>
<p>A 45<x<60
B x = 60
C 60 < x < 90
D x = 90
E x > 90</p>
<p>x must be obtuse, because the 3,4,5 triangle has x as 90 degrees, so if the side opposite the angle increases, the angle increases too. (because here instead of 3-4-5 we have 3-4-6 triangle)</p>
<p>If you want a mathematical solution , use cosine rule.
c^2 = a^2 + b^2 - 2absin@
where c is 6, a is 4, b is 3 and @ is the angle between a and b, ie. x
so 36 = 16 + 9 - 24 sin@
sin@ = 11/24
and if you calculate the value from a calculator, you'll get a value greater than pi/2 or 90 degrees (acc. to the mode selected in the calculator)</p>
<p>In short, x >90 (and less than 180)</p>
<p>Isn't it: c^2 = a^2 + b^2 - 2abcos@?</p>
<p>oh **** ya, my bad had just woken up ;) that's why it's called cosine rule lol</p>
<p>Hehe yeah. Sleeping past noon? That's not something I get to do too oftne ;)</p>