On the unit circle, at 30 degrees the point is ( sqrt(3)/2 , 1/2 )
Cosine "represents" the x value (x, y)
Therefore:
cos(30) = sqrt(3) / 2
It is highly advisable for you to memorize the unit circle -- at least the quadrant I angles (0, 30, 45, 60, and 90). I'll include a link to a good unit circle reference in the related links.
cosine(59 degrees) = 0.51504 (rounded)
cos(50) = 0.6428 (rounded)
The takeoff for a 30 degree angle will depend with the offset angle.
Yes and they are both acute angles
a 60-degree angle
As a decimal: 0.866 As a fraction: √(3)/2
cosine(59 degrees) = 0.51504 (rounded)
60 degrees = 0.5 1/2
at a 45 degree angle, or pi/4
45 degree
cos(50) = 0.6428 (rounded)
It depends on the length of the other two sides which creates that angle. Not enough information was given. However, you can simply use the Cosine rule to find it if the other two lengths are known. a2=b2+c2- 2bccosA (A=30 and a is the length of the side opposite to 30 degree angle; b and c is the length of the sides which makes up the 30 degree angle)
30 degree angle
Cos(65 deg) = 0.4226 approx.
Yes.
a 60 degree angle is twice the size of a 30 degree angle.
The takeoff for a 30 degree angle will depend with the offset angle.