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?

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.

[tex]\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}[/tex]

[tex]\text{tan}(9^{\circ})=\frac{380}{x}[/tex]

[tex]x=\frac{380}{\text{tan}(9^{\circ})}[/tex]

[tex]x=\frac{380}{0.158384440325}=2399.22557[/tex]

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

[tex]\text{tan}(5^{\circ})=\frac{380}{x+y}[/tex]

[tex]x+y=\frac{380}{\text{tan}(5^{\circ})}[/tex]

[tex]x+y=\frac{380}{0.087488663526}[/tex]

[tex]2399.22557+y=4343.419875[/tex]

[tex]y=4343.419875-2399.22557[/tex]

[tex]y=1944.194305\approx 1944.19[/tex]

Therefore, the both ships are approximately 1944.19 meters apart.

lhabdulsamirahmed lhabdulsamirahmed · Answer 2 · 2022-04-01T12:19:03+02:00

The distance of the ship from the shore is 2399.5m and the distance between the ships is 1944.2m

Data;

Height (opposite) = 380
angle = 9°

Distance of shore from ship

To calculate the distance of the shore from the ship, we can use trigonometric ratio SOHCAHTOA here since we have the value of angle and opposite side and just need to solve for the adjacent.

[tex]tan \theta = \frac{opposite}{adjacent} \\[/tex]

Let's substitute the values and solve

[tex]tan 9 = \frac{380}{x} \\x = \frac{380}{tan 9} \\x = 2399.225m[/tex]

The distance of the ship from the shore is 2399.5m

b)

The distance between the ships can also be calculated using the pervious method, only a little change is required.

[tex]tan \theta = \frac{opposite}{adjacent}\\ tan 5 = \frac{380}{x+y}[/tex]

Let's proceed to solve this

[tex]x+ y = \frac{380}{tan 5} \\x + y = 4343.42[/tex]

But we already know the value of x, let's substitute the value and solve

[tex]x + y = 4343.42\\2399.225 + y = 4343.42\\y = 4343.42 - 2399.225\\y = 1944.2m[/tex]

The distance between the ships is 1944.2m

From the calculations above, the distance of the ship from the shore is 2399.5m and the distance between the ships is 1944.2m

Learn more on trigonometric ratio here;

https://brainly.com/question/11967894