Question

The axis of a light in a lighthouse is tilted. When the light points east, it is inclined upward at 4 degree(s). When it points north, it is inclined upward at 6 degree(s). What is its maximum angle of elevation? (Hint: The maximum angle of elevation of plane of the beam above the horizontal plane is the same as the angle between the normal to the plane of the beam and the normal to the horizontal plane.)
??? degrees

Answer 1

I dunno the answer but I think the following lind could help,
http://answers.yahoo.com/question/index?qid=20110524123506AAQRiTj,http://www.freemathhelp.com/forum/threads/45968-gradient-vectors-The-axis-of-a-light-in-a-lighthouse-is-...

Answer 2

says the answer is deleted !

Answer 3

The axis of a light in a lighthouse is tilted. When the light points east, it is inclined upward at 7 degree(s). When it points north, it is inclined upward at 5 degree(s). What is its maximum angle of elevation? (Hint: The maximum angle of elevation of plane of the beam above the horizontal plane is the same as the angle between the normal to the plane of the beam and the normal to the horizontal plane.)

ANS:The vector of the light plane in east direction is (1 / 0 / 0.12278) (with 0,12278/1 = tan(7°),
the light vector in north direction = (0 / 1 / 0.087488) (with 0.087488/1 = tan(5°).
Their cross product vector is the normal vector of the light plane:
(1 / 0 / 0.12278)x(0 / 1 / 0.087488) = (- 0.12278 / - 0.087488 / 1 )

and the normal vector of the horizontal plane = (0 / 0 / 1).
Now find the dot product of the two normal vectors, divided by the product of their magnitudes, for cos(angle):
cos (angle) = (- 0.12278 / - 0.087488 / 1 )⋅(0 / 0 / 1)
/(√(0.12278^2 + 0.087488^2 + 1^2)*√1^2)

cos(angle) = 1/(1.0113) = 0.988826
angle = 8.5734°

Answer 4

I posted the similar question and its answer I found on that site.

Answer 5

didnt work

Answer 6

The second link opens..try with that.. http://www.freemathhelp.com/forum/threads/45968-gradient-vectors-The-axis-of-a-light-in-a-lighthouse-is-...

Answer 7

that didn't work either

Answer 8

I tried my best.

Answer 9

thanks either way