A ship leaves port with a bearing of S 40 W. After traveling 7 miles, the ship turns 90 degrees on a bearing of N 50 W for 11 miles. At that time, what is the bearing of the ship from port?

its the square root of 49+121

N32.47E

idk help

To determine the bearing of the ship from the port, we need to use trigonometry.

Step 1: Draw a diagram to visualize the situation. Label the starting point as the port, and mark the direction of the ship's initial bearing as S 40 W. Draw a line representing the 7-mile distance traveled by the ship.

Step 2: From the end of the 7-mile line, draw a perpendicular line. This represents the ship's turn of 90 degrees on a bearing of N 50 W. Mark the 11-mile distance traveled along this line.

Step 3: Connect the starting point (port) with the endpoint of the ship's journey so far (after the 90-degree turn). This line represents the straight-line path from the port to the current location of the ship.

Step 4: Use inverse tangent or arctan to find the angle between the straight line (port to ship's location) and the original bearing (S 40 W). This angle will give us the bearing of the ship from the port.

Step 5: Calculate the angle using the trigonometric function. In this case, the tangent of the angle between the two lines can be found by dividing the vertical distance (11 miles) by the horizontal distance (7 miles).

tan(angle) = 11/7

Step 6: Use the inverse tangent (arctan) function to find the angle. Take the arctan of the ratio calculated in step 5.

angle = arctan(11/7)

Step 7: Convert the angle to degrees using a calculator.

angle ≈ 57.7 degrees

Step 8: Determine the ship's bearing from the port by subtracting the calculated angle from the original bearing of S 40 W.

Bearing from port = S 40 W - 57.7 degrees

Therefore, the bearing of the ship from the port is approximately S 97.7 W.