A lighthouse is 9.6 nautical miles from a ship which bears 156 degrees from the lighthouse.How far is the ship east of the lighthouse?Give answer correct to one-tenth of a nautical mile.
A lighthouse is 9.6 nautical miles from a ship which bears 156 degrees from the lighthouse. How far is the ship east of the lighthouse?
8.8 n
Well, that ship sure is steering himself into quite a mathematical maze! To find out how far east the ship is from the lighthouse, we can use a little bit of trigonometry.
Since we know that the ship is 9.6 nautical miles away and the bearing is 156 degrees, we can break out our trusty trig function, the cosine. The cosine of an angle gives us the adjacent side, which in this case is how far east the ship is from the lighthouse.
So, cos(156°) = adjacent/hypotenuse
Plugging in our values, we get:
cos(156°) = x/9.6
Now, we just need to solve for x. Let's do some number crunching:
x = 9.6 * cos(156°)
After punching it in the ol' calculator, we find that the ship is approximately 6.1 nautical miles east of the lighthouse.
Ahoy, there, ship! Hope you don't encounter any math storms on your way!
To find how far the ship is east of the lighthouse, we need to use trigonometry. Specifically, we can use the cosine function to determine the horizontal distance (or east-west distance) between them.
First, let's draw a diagram to visualize the given information. Since the ship bears 156 degrees from the lighthouse, we can mark this angle between a line pointing straight north and the line connecting the ship and the lighthouse.
Now, let's use the cosine function. The cosine of an angle is equal to the adjacent side divided by the hypotenuse. In this case, the adjacent side represents the east-west distance we want to find, and the hypotenuse represents the distance between the ship and the lighthouse.
Using the formula, we have:
cos(angle) = adjacent / hypotenuse
cos(156 degrees) = adjacent / 9.6 nautical miles
To find the value of cos(156 degrees), we can use a calculator or a trigonometric table. In this case, cos(156 degrees) is approximately -0.8977.
Plugging this value into the equation, we have:
-0.8977 = adjacent / 9.6 nautical miles
To isolate the adjacent side (east-west distance), we can multiply both sides of the equation by 9.6:
-0.8977 * 9.6 = adjacent
Simplifying, we get:
-8.6219 = adjacent
However, since we're looking for a positive east-west distance, we take the absolute value:
8.6219 = |adjacent|
Therefore, the ship is approximately 8.6 nautical miles east of the lighthouse.
Lighthouse = 9.6nmi@156o.
X = 9.6*cos156 = -8.8 n. miles = 8.8 n.
miles West of ship.
Ship = 8.8 Nautical miles East of light-
h0use.