Length contraction of a ruler at 60 degrees to the observer

[dcarmichael]

Homework Statement

7. A meter stick is moving with speed 0.8c relative to a frame S .
(a) What is the stick’s length, as measured by observers in S , if the stick is parallel
to its velocity v ?
(b) What if the stick is perpendicular to v ?
(c) What if the stick is at  60 to v , as seen in the stick’s rest frame? [Hint: You can
imagine that the meter stick is the hypotenuse of a 30-60-90 right triangle]
(d) What if the stick is at  60 to v , as measured in S ?
I believe i have solved a-c , but cant figure out d, looking suggestions?

Relevant Equations

L=Lo*sqrt (1-β^2)
told to use this equation and not lorentz transformation for this problem

 

[TSny]

(d) What if the stick is at  60 to v , as measured in S ?
...cant figure out d, looking suggestions?

There are different ways to solve this. One approach is to first find the value of $\theta '$ (the angle that the stick makes to the x'-axis in the primed frame). A hint for doing that is to consider how $\tan \theta'$ is related to $\tan 60^o$.