A pilot is flying from Thunder Bay, Ontario to Dryden, Ontario a distance of approximately 320 km. As the plane leaves Thunder Bay, it flys 20° off course for exactly 80 km. After flying off-course how far is the plane from Dryden?

The plane is 246.4 kilometres from Dryden (approximately)

Step-by-step explanation: Please refer to the picture attached for further details.

The pilot was meant to fly from Thunder Bay which is marked as point T to Dryden which is marked as point D. The distance is given as approximately 320 kilometres as shown.

However upon departure, the pilot goes off course at an angle of 20 degrees and flies for 80 kilometres. When he has traveled for exactly 80 kilometres, he would find himself at point P as shown in the diagram. The plane which is now at point P, is t kilometres from Dryden (point D). To calculate the distance t, we shall apply the cosine formula, having been given two sides and an angle between.

The cosine rule states as follows;

c² = a² + b² - 2abCosC

Substituting for the given variables in this question, the formula can be expressed as follows;

t² = d² + p² - 2dpCosT

Substituting for the known values, we now have,

t² = 80² + 320² - 2(80*320)Cos20

t² = 6400 + 102400 - 2(25600)0.9396

t² = 108800 - (51200) * 0.9396

t² = 108800 - 48107.52

t² = 60692.48

Add the square root sign to both sides of the equation

√t² = √60692.48

t = 246.3584

t ≈ 246.4

Therefore, the plane is approximately 246.4 kilometres from Dryden.

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