Subjects trigonometry

Bearing Port Q 3A3Dcf

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1. **State the problem:** Aleena sails from port P on a bearing of 070° for 1.5 hours at 12 km/h to port Q. We need to find the bearing of port Q from lighthouse L. 2. **Calculate distance from P to Q:** Distance = speed \times time = $12 \times 1.5 = 18$ km. 3. **Convert distance to scale drawing units:** Scale is 1 cm = 4 km, so distance on drawing = $\frac{18}{4} = 4.5$ cm. 4. **Determine coordinates of Q relative to P:** Bearing 070° means 70° clockwise from North. - $x_Q = 18 \times \sin 70^\circ$ - $y_Q = 18 \times \cos 70^\circ$ Calculate: - $x_Q = 18 \times 0.9397 = 16.91$ km - $y_Q = 18 \times 0.3420 = 6.16$ km 5. **Position of L relative to Q:** Given L is at about 140° from Q on the protractor. 6. **Find vector from L to Q:** Since L is at 140° from Q, the bearing from L to Q is 140°. 7. **Find bearing of Q from L:** Bearing from L to Q is 140°, so bearing of Q from L is $140^\circ - 180^\circ = -40^\circ$, which corresponds to $360^\circ - 40^\circ = 320^\circ$. **Final answer:** The bearing of port Q from lighthouse L is **320°**.