How Do You Calculate Distance and Direction Using the Law of Cosines?

[finfanrb23-rw]

Homework Statement

Two geological field teams are working in a remote area. A global positioning system (GPS) tracker at their base camp shows the location of the first team as 39 km away, 11° north of west, and the second team as 30 km away, 38° east of north. When the first team uses its GPS to check the position of the second team, what does the GPS give for the following?
(a) the second team's distance from the first team
(b) the second team's direction from the first team, measured relative to due east

Homework Equations

The law of cosines

c^2=a^2 + b^2 - 2ab Cos

The Attempt at a Solution

Alright I got part a) using the law of cosines and solving for c... But for the life of me I can't figure out b)! I know it's something simple I'm overlooking, considering I have all of the sides... And one angle... Any help would be greatly appreciated...

 

[rock.freak667]

The Attempt at a Solution

Alright I got part a) using the law of cosines and solving for c... But for the life of me I can't figure out b)! I know it's something simple I'm overlooking, considering I have all of the sides... And one angle... Any help would be greatly appreciated...

You'll need to use the sine rule

$$\frac{A}{sinA}=\frac{B}{sinB}=\frac{C}{sinC}$$

 

[kerimek]

The law of cosines is a useful tool for solving problems involving triangles. In this case, we can use it to find the distance and direction between the two teams.

To solve for part b), we can use the law of cosines again, but this time we will be solving for an angle. We know the lengths of all three sides of the triangle (39 km, 30 km, and the distance between the two teams), so we can use the formula c^2 = a^2 + b^2 - 2ab cosC to find the measure of angle C, which is the angle between the two teams.

Once we have the measure of angle C, we can use basic trigonometry to find the direction of the second team from the first team. Remember that the direction is measured relative to due east, so you may need to add or subtract 90 degrees from the angle you calculated.

I hope this helps! Remember to always double check your calculations and units to ensure accuracy. Good luck with your homework!