Calculate distance of house from A

Question

The bearing of a house from point A is 319 degree.from point B, 317m due east of A ,the bearing of the house is 288 degree ,how far is the house from A?

Answer 1

Begin by drawing a horizontal segment from A to B ( pt. A is left of pt. B)

Label the length of this segment 317m

 

Start with a Vertical ray from pt. B going straight up.  Rotate this ray 

clockwise 288°, draw a line from B showing this bearing

 

Doing the same with pt. A, using a vertical line straight up from A, rotate

clockwise 319°, draw a line from A along this bearing until it intersects

bearing line you drew from pt. B

 

Label the point of intersection of the two bearing lines you drew

H for the house

 

You now have a triangle HAB with:

 

angle ABH = 18° , angle HAB =131°,  angle AHB = 31°

 

Using the Law of Sines:  sin 31° / 317 = sin 18° / HA  (distance sought)

 

solving for:  HA = 317 ( sin 18° ) / (sin 31°)

 

                 HA  = 190.196m  (distance from house to A)

Answer 2

Hello Julcit,

I am confused by the description. I don't understand the relative positions of A and B.

please confirm that you have correctly written the problem statement.

Thanks!