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X is due east point of y on a coast…

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X is due east point of y on a coast. Z is another point on the coast but 6.0km due south of Y. If the distance ZX is 12km, calculate the bearing of Z from X

A. 240°

B. 150°

C. 60°

D. 270°

QUICK ANSWER…

A

DETAILS…

If X is due east point of Y on a coast, Z is another point on the coast but 6.0km due south of Y, and the distance ZX is 12km, the bearing of Z from X will be = 240ᵒ. Let’s carefully resolve this…

First, lets sketch the problem as follows:

X is due east point of y on a coast

From the sketch, the bearing of Z from X is indicated by the arrow which will be = 270ᵒ – φ or 360ᵒ – 90 – φ

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Solving for φ, we use SOHCAHTOA

Thus,

Sine φ = opp/hyp = 6/12 = 0.5

Φ = sin¯¹0.5 = 30ᵒ

Thus, the bearing of Z from X is = 270 – 30 = 240ᵒ.

Now for the right answer to the above question:

  1. Option A is correct.
  2. Option B is not correct.
  3. C is incorrect.
  4. D is not the correct answer.

KEY-POINTS…

You may please note these/this:

  • The bearing of a point from another point is an angle formed when you draw a clockwise arrow from the north pole of the reference point to the line linking the reference point to the desired point.
  • Please observe that in the problem above, the bearing arrow was drawn from the north of X to line ZX.

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/ culled from 2021 JAMB-UTME MATHEMATICS question 38 /

1 Answers

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    The bearing of a point from another point is an angle formed when you draw a clockwise arrow from the north pole of the reference point to the line linking the reference point to the desired point.

    Admin - Mar 30, 2022 | Reply


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