A puffin leaves a cliff and flies 33 km due east then 52 km due north to an island. Work out the bearing from the cliff to the island. Give your answer to the nearest degree.
Answer (1)
The puffin's flight forms a right triangle.
Calculate the angle θ using the arctangent function: θ = arctan ( 33 52 ) .
Convert the angle to degrees.
Round the angle to the nearest degree to find the bearing: 58
Explanation
Problem Analysis Let's break down this problem. A puffin flies east and then north, forming a right-angled triangle. We need to find the bearing from the starting point (the cliff) to the final point (the island). This bearing is an angle measured clockwise from the north direction.
Visualizing the Journey We can visualize the puffin's journey as two sides of a right-angled triangle. The eastward flight is one side (33 km), and the northward flight is the other side (52 km). The bearing we want to find is the angle at the cliff, measured from north. Let's call this angle θ .
Using the Tangent Function To find the angle θ , we can use the tangent function, which relates the opposite side (northward distance) to the adjacent side (eastward distance). So, we have:
tan ( θ ) = adjacent opposite = 33 52
To find θ , we need to take the inverse tangent (arctan) of 33 52 :
θ = arctan ( 33 52 )
Calculating the Angle Now, let's calculate the value of θ in degrees. The result of the operation is approximately 57.57 degrees. Since we need to round the answer to the nearest degree, we get θ ≈ 58 degrees.
Finding the Bearing The bearing from the cliff to the island is the angle measured clockwise from North. Therefore, the bearing is approximately 58 degrees.
Examples
Bearings are commonly used in navigation, surveying, and aviation. For example, a pilot uses bearings to determine the direction to fly from one airport to another. Similarly, a surveyor uses bearings to map land boundaries and create accurate property maps. In everyday life, understanding bearings can help you navigate using a map and compass, or even interpret directions given by GPS devices.
