A plane flying a straight course observes a mountain at a bearing of 30.3degrees to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time later, the bearing to the mountain becomes 40.3degrees. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km) ?

Question

Mathematics

Danica Fritz

18 March, 12:21

A plane flying a straight course observes a mountain at a bearing of 30.3degrees to the right of its course. At that time the plane is 9 kilometers from the mountain. A short time later, the bearing to the mountain becomes 40.3degrees. How far is the plane from the mountain when the second bearing is taken (to the nearest tenth of a km) ?

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Answers (1)

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Emmy Berry · Answer 1

12km or 12 kilometers

Step-by-step explanation:

We are given the following values:

For the first bearing we have:

30.3 degrees at a distance of 9 kilometers

We are asked to find the second distance of the second bearing at 40.3 degrees

Therefore, we have:

30.3 degrees = 9km

40.3 degrees = ? Unknown (we designate this as y)

We crossmultiply

30.3 degrees * y = 9km * 40.3 degrees

Divide the both sides by 30.3 degrees

y = (9km * 40.3 degrees) : 30.3 degrees

y = 362.7/30.3 degrees

y = 11.97029703 km

Approximately to the nearest tenth of a km

y = 12km.

Therefore, the distance of the plane from the mountain when the second bearing is taken (to the nearest tenth of a km) is 12km.