Question 1.56 - I have a right triangle in the yz surface - the base is from the origin to (0,1,0), the height is from (0,1,0) to (0,1,2) and the hypotenuse is from (0,1,2) back to the origin. Why is it true that for this triangle in the yz surface - the angle theta (in spherical coordinates - the azimuth angle with the z axis) runs from pi/2 to pi/4 along the height of the triangle - from (0,1,0) to (0,1,2)? I agree that theta starts at pi/2, but if it were to end at pi/4 you were basically saying that the angle between the z axis and the hypotenuse is 45 deg right? but because the height and base of the triangle are not at the same length, it can not be (this 45 deg angle is the same as the angle between the hypotenuse and the height because the height is parallal to the z axis) ... so why theta does end at pi/4?
I refer to step (3) in the solution pic I've uploaded