Ahiker starts walking due west from sasquatch point and gets to the chupacabra trailhead before she realizes that she hasn't reset her pedometer. from the chupacabra trailhead she hikes for 5 miles along a bearing of n55°w which brings her to the muffin ridge observatory. from there, she knows a bearing of s65°e will take her straight back to sasquatch point. how far will she have to walk to get from the muffin ridge observatory to sasquatch point?

okay so u only know one distance in this triangle! but u can find all three angles and get a side angle angle or SAA triangle and can solve with the law of cosines or sines from there

what is the side? that's 5 miles

what are the angles?

given north is at 90°, 57° west of north means one angle is 90° +50° = 147°

given south is 90° -69° = 21°

third angle is 180° -147° -21° = 12°

this means 12° is opposite 5 miles

hence distance from muffin observatory to chubacabra trail is 5 miles

distance from sasquatch point to muffin observatory is found from the law of sines

d /sin(147°) = 5 /sin(12°)

d = 5 *sin(147°) /sin(12°) = 13.10 miles

then distance from sqsuqtahc point to chubacapra trail is

d /sin(21°) = 5 /sin(12°)

d = 5 *sin(21°) /sin(12°) = 8.62 miles

there is no