Mathematics: A petrol kiosk p is 12 km due north of another petrol kiosk q. The bearing of a police station r from p is 135 degree and that from q is 120 degree. Find the distance between p and r

What you would do is... 149.50 is ten right? so do 149.50 divided by 10 to find the price for each calculator. then you will multiply the cost of each calculator by 100, 1000, and 500. hope this helps :)...

A petrol kiosk p is 12 km due north of another petrol

Ответ:

scottmichetti

14.02.2022

Mathematics

Distance between P and R is 40.15 km.

Step-by-step explanation:

From the picture attached,

Petrol kiosk P is 12 km due North of another petrol kiosk Q.

Bearing of a police station R is 135° from P and 120° from Q.

m∠QPR = 180° - 135° = 45°

m∠PQR = 120°

m∠PRQ = 180° - (m∠QPR +m∠PQR)

= 180° - (45° + 120°)

= 180° - 165°

= 15°

Now we apply sine rule in ΔPQR to measure the distance between P and R.

$\frac{\text{sin}(\angle QPR)}{\text{QR}}= \frac{\text{sin}(\angle PQR)}{\text{PR}}=\frac{\text{sin}\angle PRQ}{\text{PQ}}$

$\frac{\text{sin}(45)}{\text{QR}}= \frac{\text{sin}(120)}{\text{PR}}=\frac{\text{sin}(15)}{\text{12}}$

$\frac{\text{sin}(120)}{\text{PR}}=\frac{\text{sin}(15)}{\text{12}}$

PR = $\frac{12\text{sin}(120)}{\text{sin}(15)}$

PR = 40.15 km

Therefore, distance between P and R is 40.15 km.

A petrol kiosk p is 12 km due north of another petrol kiosk q. The bearing of a police station r fro

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A petrol kiosk p is 12 km due north of another petrol kiosk q. The bearing of a police station r from p is 135 degree and that from q is 120 degree. Find the distance between p and r

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