A ship is passing through the island of corregidor. At its closest point of approach radar determine that it is 2,400 m away. Later the radar determines that it is 2,650 m away .

a.)By what angle did the ship's bearing from corregidor change ?
b.)How far did the ship travel but the two observations ?

To answer the given questions, we need to use the concept of trigonometry and apply some calculations. Here's how:

a.) By what angle did the ship's bearing from Corregidor change?

We can find the change in angle using the Law of Cosines. The formula is:

c^2 = a^2 + b^2 - 2ab * cos(C)

In this case, 'a' represents the initial distance of 2,400 m, 'b' represents the final distance of 2,650 m, and 'c' represents the change in angle.

Substituting the given values into the formula, we can solve for 'c':

c^2 = 2400^2 + 2650^2 - 2 * 2400 * 2650 * cos(C)

c^2 = 5,760,000 + 7,022,500 - 12,720,000 * cos(C)

c^2 = 12,782,500 - 12,720,000 * cos(C)

Now, rearrange the equation to solve for cos(C):

cos(C) = (12,782,500 - c^2) / (12,720,000)

Calculate the value of cos(C) by substituting the change in distance value 'c' into the equation:

cos(C) = (12,782,500 - c^2) / (12,720,000)

Finally, calculate the angle 'C' using the inverse cosine function (arccos) to find the angle in degrees.

b.) How far did the ship travel between the two observations?

To find the distance traveled by the ship, we can simply subtract the initial distance from the final distance:

Distance traveled = Final distance - Initial distance

Distance traveled = 2,650 m - 2,400 m

Distance traveled = 250 m

Therefore, the ship traveled 250 meters between the two observations.