If Jeff and Carl are 500 feet apart, how far is Jeff from the Sasquatch nest? Round your answer to the nearest foot.

Question

Carl spies a potential Sasquatch nest at a bearing of N10(degrees)E and radios Jeff, who is at a bearing of N50(degrees)E from Carl’s position. From Jeff’s position, the nest is at a bearing of S70(degrees)W.

Answer 1

The Sasquatch's nest is where the 3 green stars (***) are in the picture in the link here: 1drv.ms/u/s!AvQhCl0SMET3x0riInhhAlJPwE_u?e=1tSgog.

To find the distance from Jeff to the nest (X in the picture above), we must first find the angles of the completed triangle in the picture below, via the following:

1) The angle in that completed triangle that is nearest to Carl and opposite from the distance X is 50° - 10° = 40°.

2) The angle between the line from Carl to Jeff and the line from Carl out to the East is 90° - 50° = 40°.

3) Now, since the angle between the directions South and East is 90°, then the angle between the line from Jeff to Carl and the line from Jeff down to the South is 180° - 90° - 40° = 50°.

4) Next, the angle between the line from Jeff to Carl and the line from Jeff to the Sasquatch's nest is 70° - 50° = 20°.

5) Finally, the angle opposite the line from Jeff to Carl is 180° - 40° - 20° = 120°.

Now, since you have all 3 angles of the completed triangle below, then you can find the distance X from the Law of Sines formula:

distance from Jeff to Carl distance from Jeff to nest

------------------------------------------------- = -------------------------------------------------

sine of opposite angle of that line sine of opposite angle of that line

So, we now have:

500 ft X

------------- = --------------- ---> X = 500 ft * sin(40°) / sin(120°) ≈ 371 ft

sin(120°) sin(40°) [rounded to the nearest foot]