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3 years ago

Hi:) how to do this?

Mathematics

1 answer:

Katen [24]3 years ago

4 0

Answer:

b) 15.2km

c) Bearing= 263.8° (1 d.p.),

AD= 25.5 km (3 s.f.)

Step-by-step explanation:

Please see attached picture for full solution.

In picture 3, you could also use trigonometry to find AW, just like how we did to find W.

Picture 4:

WD= 16 -15.250

WD= 0.75

Picture 5:

Bearing of D from A

= reflex ∠N₂AD

= 295° - ∠BAD

∠BAD

= ∠BAW -∠WAD

= 33° -1.829°

= 31.171°

Thus, bearing of D from A

= 295° - 31.171°

= 263.8° (1 d.p.)

c) Distance of D from A= length AD

Look at triangle BAD:

∠DBA= 65°

∠ADB= 180° -65° -31.171° (∠ sum of △ADB)

∠ADB= 83.829°

Using sine rule,

$\frac{sin∠ABD}{AD} = \frac{sin∠ADB}{AB} \\ \frac{sin65°}{AD} = \frac{sin83.829°}{28} \\ AD(sin83.829°) = 28(sin65)° \\ AD = \frac{28(sin65°)}{sin83.829°} \\ AD = 25.5km \: (3 \: s.f.)$

Feel free to ask if you have any queries :)

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