A distressed ship is 10 miles south and 8 miles east of a coast guard station.

a) What bearing should the coast guard boat take to reach the distressed ship?
b)How many miles will the coast guard boat travel?
c)If the coast guard boat is traveling 30 miles per hour, how long will it take for the boat to reach the distressed ship?
d)What bearing should the boat take to return to the coast guard station?

Please help I just came back from break and I completely forgot how to solve these kinds of problems!

X = 8 Mi

Y = -10 Mi

a. Tan A = Y/X = -10/8 = -1.25
A = -51.3o = 51.3o S. of E.

b. d^2 = X^2 + Y^2 = 8^2 + (-10)^2 = 164
d = 12.81 Miles.

c. d = V*t
Solve for t.

d. A = -51.3 + 180 = 128.7o, CCW = 51.3o
N. of W.

No worries, I'll walk you through the steps to solve each part of the problem.

a) To determine the bearing the coast guard boat should take to reach the distressed ship, we can use trigonometry. We can find the angle between the horizontal axis and the line connecting the coast guard station and the distressed ship.

First, we calculate the angle using the tangent function. The tangent of an angle is equal to the ratio of the opposite side to the adjacent side. In this case, the opposite side is 10 miles (the southward distance) and the adjacent side is 8 miles (the eastward distance).

So, the angle (bearing) can be found by taking the inverse tangent (arctan) of (10/8) using a scientific calculator.

b) To find how many miles the coast guard boat will travel, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the distance traveled by the boat) is equal to the sum of the squares of the other two sides (the distances traveled south and east).

In this case, the distance traveled south is 10 miles and the distance traveled east is 8 miles. So, the hypotenuse (total distance traveled by the boat) can be calculated as the square root of (10^2 + 8^2).

c) To calculate the time it will take for the boat to reach the distressed ship, we need to divide the distance (calculated in part b) by the speed of the boat. In this case, the speed is given as 30 miles per hour.

So, we divide the distance calculated in part b by the speed to get the time. Remember to keep the units consistent, so if the distance is in miles, the speed should also be in miles per hour.

d) To determine the bearing the boat should take to return to the coast guard station from the distressed ship, we need to use the inverse of the bearing calculated in part a. Essentially, if the boat traveled on a certain bearing to reach the distressed ship, it needs to travel in the opposite direction to return to the coast guard station. So if the bearing calculated in part a was N degrees, the bearing to return will be N+180 degrees.

I hope this helps! Let me know if you have any additional questions.