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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:
From the sketch, the bearing of Z from X is indicated by the arrow which will be = 270ᵒ – φ or 360ᵒ – 90 – φ
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:
- Option A is correct.
- Option B is not correct.
- C is incorrect.
- 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 /
