Question

Standing on a cliff 380 meters above the sea, Pat sees an approaching ship and measures its angle of depression, obtaining 9 degrees.
a) How far from shore is the ship?

b) Pat sights a second ship beyond the first. the angle of depression of the second ship is 5 degrees. How far apart are the ships?

Answer 1

Answer:

(a). 2399.23 meters.

(b). 1944.19 meters apart.

Step-by-step explanation:

Please find the attachment.

We have been given that standing on a cliff 380 meters above the sea, Pat sees an approaching ship and measures its angle of depression, obtaining 9 degrees.

(a) We are asked to find how far from the shore is the ship.

We know that tangent relates opposite side of a right triangle with its adjacent side.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

$\text{tan}(9^{\circ})=\frac{380}{x}$

$x=\frac{380}{\text{tan}(9^{\circ})}$

$x=\frac{380}{0.158384440325}=2399.22557$

Therefore, the ship is approximately 2399.23 meters away from the shore.

$\text{tan}(5^{\circ})=\frac{380}{x+y}$

$x+y=\frac{380}{\text{tan}(5^{\circ})}$

$x+y=\frac{380}{0.087488663526}$

$2399.22557+y=4343.419875$

$y=4343.419875-2399.22557$

$y=1944.194305\approx 1944.19$

Therefore, the both ships are approximately 1944.19 meters apart.