High School

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While following the directions on a treasure map, a pirate walks 39.4 m north, then turns and walks 1.5 m east. At what angle with the north would he have to walk?

A) 2.43 degrees
B) 87.57 degrees
C) 177.57 degrees
D) 92.43 degrees

Answer :

Final answer:

The pirate would need to walk at an angle approximately equal to 2.43 degrees to the north. This is calculated using the tangent rule in trigonometry, considering that the pirate first walks north and then east.

Explanation:

Solution

In this problem, the pirate first walks 39.4 m north, and then moves 1.5 m east. Using these values, we need to find the angle the pirate will have move at compared to the initial north direction.

This can be solved using the tangent rule in trigonometry. Specifically, the tangent of the angle (Θ) between the north and the direction he needs to walk is given by, tan(Θ) = east/north = 1.5m/39.4m.

To find the angle value Θ, we can use the inverse tangent function, noted as arctan() or tan-1(). Calculating this gives approximately Θ = 2.17°.

The closest of the options given is A) 2.43 degrees, which can be considered as a suitable answer giving an approximate value, if we consider the distances to be estimates. However, this degree of approximation should ideally be confirmed in a real classroom setting.

Learn more about Trigonometry here:

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