# Math Help - bearings

1. ## bearings

An overhead power cable 8000 metres miles long travels due north. Another cable starts from the south end of this in a direction N. 24° E. A third cable starts from the north end of the first one and travels in a direction S. 54° E. Find the length of this cable if it travels in a straight line to meet the second cable, and find the distance of the junction
from the line of the first cable.

thanks

2. Originally Posted by Steven H
An overhead power cable 8000 metres miles long travels due north. Another cable starts from the south end of this in a direction N. 24° E. A third cable starts from the north end of the first one and travels in a direction S. 54° E. Find the length of this cable if it travels in a straight line to meet the second cable, and find the distance of the junction
from the line of the first cable.

thanks
1. Draw a sketch

2. Calculate the value of angle $\gamma$

3. Use Sine Rule to calculate the distances x and s:

$\frac x{8000} = \frac{\sin(24^\circ)}{\sin(\gamma)}$ Solve for x.

$\frac s{8000} = \frac{\sin(54^\circ)}{\sin(\gamma)}$ Solve for s.

3. Originally Posted by Steven H
An overhead power cable 8000 metres miles long travels due north. Another cable starts from the south end of this in a direction N. 24° E. A third cable starts from the north end of the first one and travels in a direction S. 54° E. Find the length of this cable if it travels in a straight line to meet the second cable, and find the distance of the junction

from the line of the first cable.

thanks
A drawing would be nice. I'm confused about your direction of the third cable from the North. To travel SE, wouldn't the degrees be between 90 and 180, unless you mean 54 degrees south of east. In which case the direction would be 144 degees (90+54). Otherwise 54 degrees is NE. Maybe it's just me.

4. Originally Posted by masters
A drawing would be nice. I'm confused about your direction of the third cable from the North. To travel SE, wouldn't the degrees be between 90 and 180, unless you mean 54 degrees south of east. In which case the direction would be 144 degees (90+54). Otherwise 54 degrees is NE. Maybe it's just me.

the cable is traveling in a south east direction, i think this should help, i got this from the part where is staes that the third cable starts at the north end on the first one.

thanks