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The trigonometric relations hold for right triangles. When you say Sin 30 = 1/2, you are assuming that there is a RIGHT angle there. That's how you get the hypotenuse. This triangle has no right angle yet. How did you decide that hypotenuse is x? Hypotenuse is the side opposite the 90 degrees angle. There is no angle that is 90 degrees here. BTW, good explanation by Spidy001. I am a little curious - what's the OE? Do they use trigonometry or something similar?
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The two isoscales base angles are 75 degrees each. Cos (45+30) = Cos (45) Cos (30) - Sin(45) Sin(30) Cos(75) = (\sqrt{3} - 1)/2 = 1/\sqrt{2}x

Hence, x = \sqrt{3}+1

Answer B.

Cheers!
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