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

The instrument is:

The cliff is:

The ship is at

In right triangleCode: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 ??