Rabea and Bert decide to take their forest friends for a cruise. Partway through the trip they spot a polar bear stuck on a melting iceberg in the distance! `` Rabea calculates that the polar bear is 200200 mm North, and 160160 mm East. If this ship is currently travelling at a true bearing of 000∘000 ∘ , at what true bearing must they travel to save the polar bear? Round your answer to the nearest whole number. Remember to write your answer in the appropriate format and include units.

To solve this problem, we need to use trigonometry.

Step 1: We know that the polar bear is 200 mm North and 160 mm East. This forms a right triangle where 200 mm is the opposite side and 160 mm is the adjacent side.

Step 2: We need to find the angle of this triangle to know the true bearing. We can use the tangent function for this. The formula for tangent is opposite/adjacent.

Step 3: So, tan(θ) = 200/160 = 1.25

Step 4: To find the angle θ, we need to find the inverse tangent (also known as arctan) of 1.25.

Step 5: θ = arctan(1.25) = 51.34 degrees

Step 6: Since the ship is currently traveling at a true bearing of 000 degrees, we need to adjust our answer to reflect this.

Step 7: The true bearing to save the polar bear would be 90 degrees (due East) plus our calculated angle.

Step 8: So, the true bearing = 90 + 51.34 = 141.34 degrees

Step 9: Round this to the nearest whole number, we get 141 degrees.

So, to save the polar bear, they must travel at a true bearing of 141 degrees.