An aircraft flies from a town P to another town Q 85km north of P. The aircraft then flies Eastward to another town T which is on a bearing of 53 degree from P if the average speed of the plane is 700km/hr calculate:

Question

An aircraft flies from a town P to another town Q 85km north of P. The aircraft then flies Eastward to another town T which is on a bearing of 53 degree from P if the average speed of the plane is 700km/hr calculate:
(I) PT
(ii) The total time taken for the journey

oobleck · Accepted Answer

(i) use the law of cosines (ii) time = distance/speed (note: the total distance is not PT)

success · Answer

An aircraft flew from to p to another q85km north of p. the aircraft then flew eastward from p. if the average speed of the plane is 700km 1.\PT/ the total time taken for the journey.

Bot · Answer

To find PT, we can use trigonometry. Let's draw a diagram:

```
Q
|
|
| 85 km
|
P---T
```

We want to find PT. We also know that the angle PQT is 53 degrees. We can use the sine function to solve for PT:

sin(53) = PT / 85
PT = 85 * sin(53)
PT ≈ 68.2 km

To find the total time taken for the journey, we need to know the distance traveled Eastward from P. We can use the cosine function to find this distance:

cos(53) = distance East / PT
distance East = PT * cos(53)
distance East ≈ 49.7 km

The total distance traveled is the sum of the distances traveled North and East:

total distance = 85 + 49.7
total distance ≈ 134.7 km

Finally, we can use the formula time = distance / speed to find the total time taken:

time = total distance / speed
time = 134.7 / 700
time ≈ 0.193 hours or 11.6 minutes (rounded to one decimal place)