SOLUTION: Savio is on a hiking trip. On the first section of the hike, he walks 5 km from the Loon Campsite to the Owl Campsite. Then, he turns and hikes 7 km to the Eagle Campsite, makin

Question 1160701: Savio is on a hiking trip. On the first section
of the hike, he walks 5 km from the Loon
Campsite to the Owl Campsite. Then, he turns
and hikes 7 km to the Eagle Campsite, making
a 68° angle from the first section of the hike.
He then returns on the trail to the Loon
Campsite.
a) What is the distance from the Eagle
campsite to the Loon campsite, to the
nearest kilometre?
b) At what angles are the three campsites
situated with respect to each other?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Draw this with Loon to right, Owl to the left and Eagle above Loon
Law of cosines: c^2 (the distance from E to L)=a^2+b^2-2ab cos C
c^2=74-70 cos 68=74-26.22
=47.78
c=6.91 km or 7 km
Law of Sines
6.91/sin 68=7/sin x
sin x=7 sin 68/6.91=69.93 degrees for Owl Loon Eagle angle
the third should be 42.07 degrees
6.91/sin 68=5/ sin x
so sin x=5 sin 68/6.91
=0.6709
sin(-1) 0.6709=42.13 degrees, within rounding error
so angles are from O-L-E counterclockwise 68-70-42 degrees
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