Thread: i need help fast....x

im really stuck on this question could some one plz help me solve it.

An observer sees a ship from the top of a cliff of height 100 m. The ship is seen
through an instrument which measured the angle of depression to be 80

°. The observer
then moved back a distance of 10 m, at which point the ship and the top of the cliff

were in line. Find the distance from the base of the cliff to the ship.

thanx
xxx

Hello, Steph!

A challenging problem . . .
. . and I got some strange answers.

An observer sees a ship from the top of a cliff of height 100 m.
The ship is seen through an instrument which measured the angle of depression to be 80°.
The observer then moved back a distance of 10 m, at which point the ship
and the top of the cliff were in line.
Find the distance from the base of the cliff to the ship.

I assume that the instrument has a height

Code:

           A* - - - - - - - - - - - - E
            | *  80°
          h |   *
            |     *
           B*       *
            |         *
            |           *
            |             *
        100 |               *
            |                 *
            |                   *
            |                     *
           C* - - - - - - - - - - - * D
                        x

The instrument is:
The cliff is:
The ship is at

In right triangle

Code:

    A'       A
    *       *
    | *     |
  h |   *   |
    |     * |
  B'* - - - *B
       10   |  *
            |     *
            |        *
        100 |           *
            |              *
            |                 *
            |                    *
           C* - - - - - - - - - - - *D
                        x

The observer (and the instrument) moves 10 m to
. . and are collinear.

Since


Equate [1] and [2]: .

Quadratic Formula: .


The positive root is: .


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Substitute into [1]: . m ??

Let me understand this . . .

The ship is less than 25 meters from the cliff,
. . but the instrument is over 130 feet high ??