A boat leaves the entrance to a harbor and travels 150 miles on a bearing of Upper N 56 degrees Upper E. How many miles north and how many miles east from the harbor has the boat traveled?

It can be helpful to draw a diagram. In the attached diagram, point H represents the harbor, point B represents the position of the boat, and point N represents a point directly north of the harbor and west of the boat.

The bearing N56E means the direction of travel is along a path that is 56° clockwise (toward the east) from north.

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The mnemonic SOH CAH TOA reminds you of the relationships between the sides of a right triangle. Here, we are given the length of the hypotenuse, and we want to know the lengths of the sides opposite and adjacent to the angle. One of the useful relations is ...

Sin = Opposite/Hypotenuse

In our diagram, this would be ...

sin(56°) = BN/BH

We want to find length BN, so we can multiply by BH to get ...

BN = BH·sin(56°) = 150·0.829038 = 124.4 . . . . miles (east)

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For the adjacent side, we use the relation ...

Cos = Adjacent/Hypotenuse

cos(56°) = HN/HB

HN = HB·cos(56°) = 150·0.559193 = 83.9 . . . . miles (north)

The boat has traveled 124.4 miles north and 83.9 miles east of the harbor entrance.

A boat leaves the entrance to a harbor and travels 150 miles on a bearing of Upper N 56 degrees Upper E. How many miles north and how many miles east from the harbor has the boat​ traveled?

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A boat leaves the entrance to a harbor and travels 150 miles on a bearing of Upper N 56 degrees Upper E. How many miles north and how many miles east from the harbor has the boat traveled?