Final answer:
To determine the bearing from the cliff to the island, use trigonometry and the concept of vectors. Draw a diagram, find the length of the hypotenuse, and calculate the angle using trigonometry. The bearing from the cliff to the island is approximately 58.5° east of north.
Step-by-step explanation:
To determine the bearing from the cliff to the island, we can use trigonometry and the concept of vectors.
First, let's draw a diagram of the situation:
- Draw a line representing the puffin's flight path from the cliff to the island.
- Label the length of the eastward flight as 34 km.
- Label the length of the northward flight as 56 km.
- Draw a right triangle with the eastward flight as the adjacent side and the northward flight as the opposite side.
- Use the Pythagorean theorem to find the length of the hypotenuse, which represents the direct distance from the cliff to the island.
- The bearing from the cliff to the island is the angle formed between the eastward flight and the hypotenuse.
Using the Pythagorean theorem, we can find the length of the hypotenuse:
c² = a² + b²
c² = 34² + 56²
c² = 1156 + 3136
c² = 4292
c = √4292
c ≈ 65.6 km
Now, we can find the angle using trigonometry:
tan(angle) = opposite/adjacent
tan(angle) = 56/34
angle ≈ 58.5°
Therefore, the bearing from the cliff to the island is approximately 58.5° east of north.