Question

From the top of a cliff 426 feet high, the angle of depression of a ship is observed to be 18.2°. how far out is the ship? 140 ft. 1,296 ft. 1,364 ft.

Answer 1

If we are to connect both tips of the cliff to the approaching ship, we form a right triangle. The height of the cliff is the opposite side of the angle of depression. The trigonometric function that would allow us to solve for the distance is tangent.
tan 18.2° = opposite /adjacent = 426 ft/ x ft
The value of x from the equation is 1295.68 ft
Thus, the answer is the second choice.

Answer 2

1,296 ft.

Explanation:

I did a scheme of the situation in the picture below. Now, the angle α and the depression angle add 90°. Then,

α+18.2 = 90

α = 90-18.2

α = 71.8°.

On the other hand, to find the distance x (how far out is the ship) we can use the formula of tangent of an angle. Let's find the tangent of α to find x:

tan(α)= op/ad

where op is the opposite leg and ad is the adjacent leg, then

`tan(\alpha) = (x)/(426)`

`tan(71.8) = (x)/(426)`

`tan(71.8)*426 = x`

`3.0415*426 = x`

`1295.68 = x`

Then, the cliff is 1295.68≈1296 feets far of the ship.