Can anyone help me with proofs regarding circle theorems?

Question

a man is walking along a straight road heading north when he spots the top of a tower in the direction NxºE, behind low lying trees. The angle of elevation to the top of the tower is yº. After walking d meters along the road he notices that the tower is now NzºE of the road and that the angle of elevation of the top of the tower is now aº. Let the height of the tower be h meters.

How much further must he walk before the tower is located in an easterly direction?

Answer 1

I'm not sure what is going on here because it seems you are given far too much information.

In any case, this is what I see.

Assume for convenience that the Y axis is aligned North-South and that the first observation is at the origin (Y = 0)

For the first observation, he has both a bearing and an azimuth. The bearing defines a line on the plane through the origin; the tower is somewhere on that line.

Now consider the triangle formed by the origin, the base of the tower, and the top of the tower. If we assume the land is flat, then this is a right triangle. We have one side (the height of the tower) and the opposite angle (the azimuth), so we can compute the other sides. This gives us the distance to the tower.

With angle and distance, we know exactly where the tower is (after conversion from radial to Cartesian coordinates)

This should tell us how many meters he needs to walk due due North (along the Y axis) until the tower is due East (i.e. has the same Y value).

So there is no reason for the second bearing at all, assuming the land is flat.

If the land is not flat, then the first bearing gives you one line; the second bearing gives you another line; and the intersection of the two lines gives you the location of the tower. Then, again, you know how much further North the man has to go.

But in this case, you don't need to use the angles of elevation at all.

Also, I don't understand the connection between the problem and the title. What proofs do we need here?

HTH.

Answer 2

Draw a appropriate triangle ABC.Draw a perpendicular to the hypotenuse from the alternative vertex and then information the thought by similarity. i won't be able to supply u the information as i won't be able to caricature the diagram yet u can discover it in any 10th customary e book.