Trigonometry in Navigation Problems

The video tutorial explains a bearing problem involving a ship's journey. The ship departs from a port, travels due west for 30 nautical miles, then changes course to travel south 30 degrees west for 50 nautical miles. The task is to find the bearing back to the port of departure. The instructor sets up the problem using bearings and directions, creates right triangles, and uses trigonometry to calculate distances and angles. The final bearing is determined using inverse tangent calculations, concluding with the ship's heading back to the port.

What is the initial direction the ship travels from the port?

• West

• South

• East

• North

After traveling due west, the ship changes its course. What is the new direction?

• North 30 degrees East

• North 30 degrees West

• South 30 degrees West

• South 30 degrees East

What is the total distance the ship travels after changing its course?

• 15 nautical miles

• 30 nautical miles

• 50 nautical miles

• 60 nautical miles

Why is it important to form a right triangle when solving the bearing problem?

• To simplify the calculations

• To use trigonometric functions

• To measure angles accurately

• To avoid errors

Which trigonometric function is used to find the adjacent side in the triangle?

• Tangent

• Cosine

• Secant

• Sine

What is the value of the cosine of 60 degrees used in the calculations?

• 0.707

• 1

• 0.866

• 0.5

What is the calculated length of the side opposite the 60-degree angle?

• 43.30 nautical miles

• 55 nautical miles

• 50 nautical miles

• 25 nautical miles

Which trigonometric function is used to determine the final bearing angle?

• Tangent

• Sine

• Cosine

• Cotangent

What is the final bearing angle calculated to return to the port?

• 51.78 degrees

• 60 degrees

• 30 degrees

• 45 degrees

In which direction does the final bearing angle point to return to the port?

• South 51.78 degrees West

• North 51.78 degrees East

• North 51.78 degrees West

• South 51.78 degrees East