The angle between a line and a plane is thirty degrees. Segment $MN$ on the line has length $10$. What is the length of $MN's$ orthogonal projection on the plane?
I got 5 as an answer. Is that correct? I did the following:
$sin(30) = \frac{x}{10}$ which is 5.
If the incident angle is 30 degrees, the ratio between unit length on the incident line and unit length on the orthogonal projection (the shadow cast from a light perpendicular to the plane) is the cosine(30) (the ratio of the adjacent side of the triangle to the hypotenuse):
$$ \cos(30) = \frac{\sqrt{3}}{2} $$ so, the length of the projection from a line of 10 units long is $$10\cos(30) = 5\sqrt{3}$$