A party of bush walkers have an average speed of 50km/minute and walk for 4 hours on a bearing of 231°T. they then walk for 6(1)/(3) hours on a bearing of 117°T. Find a.How far are they from bas e camp?

b. The bearing they must travel along to get to base camp

I assume the speed of the adventurers are 50 m/min. since 50km/min is almost the speed of a supersonic jet.

Also, not clear about the 6(1)/(3) hours. I take it at face value of 2 hours.

The bearing of 231°T will be assumed to be measured from true north, clockwise, equivalent to "azimuth" used in US and French speaking countries.

The solution here lies in the resolution of all distances travelled to directions east (x-axis) and north (y-axis). The components can then be summed together to get the final destination and direction, if required.

There is a little problem combining bearings and trigonometry, the latter measures angles from zero in the east direction counter clockwise.

So to calculate sines and cosines using trigonometry, and with x≡East and Y≡North, we subtract the bearing from 90°.

For example, a bearing of 117° will be calculated as (90-117)=-27° in trigonometry.

Now we're ready to sum the distances:

The distances are:
1. 4*60*50=12000m
2. 2*60*50=6000m

Bearing Angle
231°T -> 90-231=-141°
117°T -> 90-117=-27°

leg Distance(D) Angle(A) Dcos(A) Dsin(A)
1 12000 -141° -9325.75 -7551.84
2 6000 -27° 5346.04 -2723.94
Sum (x2,y2)=(-3979.71,-10275.78)
Distance = sqrt(x2²+y2²)
angle
= arctan(-10275.78/-3979.71)
Note that since both numbers are negative, angle is in 3rd quadrant
= 248.83°(trig.)
convert to bearing, subtract from 90 and add 360 if result is negative
= (90-248.83)+360
= 201.17°T

Check all calculations please.

Thank you so much for all your help you my friend are a legend! Sorry about the mistakes :0

To find the distance from base camp, we can first calculate the total time taken by the bush walkers. Then, we can use the average speed and the time taken to find the distance traveled.

Step 1: Calculate the total time taken
The party walks for 4 hours on a bearing of 231°T and 6(1)/(3) hours on a bearing of 117°T. To find the total time taken, we can add these two durations:
Total time taken = 4 hours + 6(1)/(3) hours

Step 2: Convert the time taken to minutes
To make calculations easier, let's convert the total time taken to minutes. Since there are 60 minutes in an hour, we can multiply the total time taken by 60:
Total time in minutes = (4 hours + 6(1)/(3) hours) * 60 minutes/hour

Now that we have the total time taken in minutes, we can calculate the distance from base camp.

Step 3: Calculate the distance traveled
To find the distance, we can multiply the average speed by the total time taken:
Distance = Average speed * Total time in minutes

By substituting the given average speed and the calculated total time in minutes, we can find the distance traveled.

Now let's move on to finding the bearing to base camp.

Step 4: Calculate the bearing to base camp
To find the bearing to base camp, we can use trigonometry. We will use the given bearings (231°T and 117°T) to determine the angles formed relative to the north and then find the angle between these two angles (bearing to base camp).

To calculate the bearing to base camp, follow these steps:
1. Subtract the bearing of 231°T from 360° to find the angle relative to the north for the first leg.
2. Subtract the bearing of 117°T from 360° to find the angle relative to the north for the second leg.
3. Add the two angles obtained in steps 1 and 2 to find the total angle relative to the north.
4. Subtract the total angle relative to the north from 360° to find the bearing to base camp.

By performing these calculations, we can find the bearing to base camp.

Please provide the calculations which you have for a more accurate answer.