Answer
The new length is about 0.63 meters.
Work Step by Step
We can use the length contraction equation using the component of the meter stick parallel to the x-axis.
$L_x=L_{x0} \sqrt{1-\beta^2}$
$L_x=1m*\cos30^{\circ} \sqrt{1-(.90)^2}$
$L_x=0.38m$
Now we can use the Pythagorean theorem to find the overall length:
$L=\sqrt{L_x^2+ L_y^2}$
$L=\sqrt{(0.38m)^2+ (1m*sin30^{\circ})^2}$
$L \approx 0.63m$
