A puffin leaves a cliff and flies 38 km due east then 54km due north to an island Work out the bearing from the cliff to the island. Give your answer to the nearest degree

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A puffin leaves a cliff and flies 38 km due east then 54km due north to an island Work out the bearing from the cliff to the island. Give your answer to the nearest degree

Answer 1

After rounding the complete bearing (Following step3: Calculating the bearing) ### Bearing from north = \(360° - 55° = 305° \). Therefore, the correct answer after rounding to the nearest degree is \(\boxed{305°}\). The puffin is flying with the bearing of \(305°\) from the cliff to the island.

Answer 2

## Step1: Determine the right-angled triangle The problem presents a scenario where a puffin covers a certain distance in the eastern direction, and then covers a certain distance in the northern direction. This sequence of movements forms a right-angled triangle where the puffin first travels east in a straight line (East becomes our base or adjacent side of our right triangle), then flies a vertical, straight-line distance north (excelled positioned as our height or opposite side of our right triangle), making both lines perpendicular to each other. The puffin's path from the cliff to the island corresponds to the hypotenuse of the triangle. ## Step2: Use the right triangle trigonometry to calculate the angle We'll use right triangle trigonometry to solve this. The displacement in the east-walk is the adjacent side of our given angle and the displacement in the north is the opposite. The bearing from the cliff to the island is equal to the angle \(\theta\) which the direction of travel makes with the Buestern direction (since the Bearings are always measured clockwise from the North). We will apply the tangent of the angle \(\theta\) calculated as: ### \(\tan(\theta) = \frac{{\text{{Opposite}}}}{{\text{{Adjacent}}}} \) We need to find out the value of \(\theta\). Therefore, we can rearrange the equation as: ### \(\theta = \tan^{-1}\left(\frac{{\text{{Opposite}}}}{{\text{{Adjacent}}}} \right) \) Replace the given values (Opposite = 54, Adjacent = 38) into our rearranged formula to find out the angle \(\theta\). ## Step3: Calculate the Bearing ultimately Bearing values are measured from the north and are moving in the clockwise direction. Therefore, to calculate final bearing from the cliff to the island we around 360 subtract our calculated angle: ### Bearing from north = \(360^0 - \theta^0\). # Calculation: We begin to perform the calculation by replacement of values: ### \(\theta = \tan^{-1}( \frac{{54km}}{{38km}} )\) This gives a θ of approximately 55 degrees

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A puffin leaves a cliff and flies 38 km due east then 54km due north to an island Work out the bearing from the cliff to the island. Give your answer to the nearest degree

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