Compass bearings of a carin are taken from two points A and B, 400 m apart, along a strsight north-south path, A being due north of B. the bearings of the carin from A and B are 110 degrees and 80 degrees, respectively. choose the two options which give the distances from A and B to the carin, correct to the nearest metre.

A. 402 m

B. 752 m

C. 757 m

D. 769 m

E. 787 m

F. 788 m

G. 877 m

H 878 m

is it F and G is this correct??

I marked C to be the cairn, and the angle C was 30º
Using the sine law, I got AC = 788 and BC=752
which would be B and F

To find the distances from points A and B to the cairn, let's use trigonometry and the given bearings.

First, let's label the angles at the cairn C. Looking at the information provided, we can deduce that angle BAC (the angle between points A and C) is 80 degrees, and angle ABC (the angle between points B and C) is 110 degrees.

Now, we can use the sine rule to find the distances AC and BC. The sine rule states that in any triangle:

a/sin(A) = b/sin(B) = c/sin(C)

In our case, we have:
AC/sin(BAC) = AB/sin(ABC) = BC/sin(C)

Using this formula, we can solve for the distances AC and BC.

For AC:
AC/sin(80) = 400/sin(110)
AC = (sin(80) * 400) / sin(110)
AC ≈ 787 meters (rounded to the nearest meter)

For BC:
BC/sin(110) = 400/sin(80)
BC = (sin(110) * 400) / sin(80)
BC ≈ 752 meters (rounded to the nearest meter)

So, the correct options are:

F. 788 m (distance from A to the cairn)
G. 752 m (distance from B to the cairn)