Question

An aeroplane travels on a bearing of 295o so that it is 200 km west of its starting point. How far has it travelled on this bearing?
please use diagrams to explain

Answer 1

Answer: Approximately 221 km

The more accurate value is roughly 220.675583792499 km but even that isn't an exact value.

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Explanation:

Refer to the diagram below.

The plane starts at point A, which is the origin (0,0)

Directly north is the bearing 0 degrees, which it sometimes written as triple zeros and a degree symbol at the end, so we'd write 000° to mean directly north.

Let's say we face directly north. When turning clockwise (turn toward the east), the bearing angle increases. That means directly east is the bearing 090° and 180° is directly south.

The bearing 270° is directly west. Another 25 degrees gets us to 270+25 = 295°

This plane is facing the northwest direction, as the diagram indicates below (the plane is aimed at point C while it's located at point A initially).

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Triangle ABC has the horizontal component AB = 200 km, since we're told that the plane is 200 km west of its starting point (and some unknown distance north of the starting point).

We use the cosine ratio to help determine the hypotenuse length AC

cos(angle) = adjacent/hypotenuse

cos(A) = AB/AC

cos(25) = 200/x

x*cos(25) = 200

x = 200/cos(25)

x = 220.675583792499 which is approximate.

x = 221

I'm rounding to the nearest whole number since every other value given to you is a whole number. Round as your teacher instructs.

This means the plane is roughly 221 km away from its starting point. In other words, side AC is about 221 km long.