SOLUTION: Hilary and Dale leave camp and go for a long hike. After going 7 km due east, they turn and go another 8 km in the direction 60 degrees north of east. They plan to return along a s

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Hilary and Dale leave camp and go for a long hike. After going 7 km due east, they turn and go another 8 km in the direction 60 degrees north of east. They plan to return along a s      Log On

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Question 1157506: Hilary and Dale leave camp and go for a long hike. After going 7 km due east, they turn and go another 8 km in the direction 60 degrees north of east. They plan to return along a straight path. How far from camp are they at this point? Use an angle to describe the direction that Hilary and Dale should follow to reach their camp.
Answer by KMST(5422) About Me  (Show Source):
You can put this solution on YOUR website!

We are given angle%28BAD%29=60%5Eo , CA=7km and AB=8km
From right triangle ABD, we get
BD=%288km%29%2Asin%2860%5Eo%29=%288km%29%28sqrt%283%29%2F2%29=4sqrt%283%29km
AD=%288km%29%2Acos%2860%5Eo%29=%288km%29%281%2F2%29=4km
For right triangle CBD, we have CD=CA%2BAD=7km%2B4km=11km
From right triangle CBD, we get
BC=sqrt%28CD%5E2%2BBD%5E2%29=sqrt%2811%5E2%2B%284sqrt%283%29%5E2%29%29km%22=%22sqrt%28121%2B48%29km%22=%22sqrt%28169%29km%22=%22highlight%2813km%29
tan%28red%28alpha%29%29=BD%2FCD=4sqrt%283%29%2F11=approximately0.6298 --> red%28alpha%29=approximatelyhighlight%2832.20%5Eo%29
Hilary and Dale should walk in a direction 60 highlight%2832.20%5Eo%29 south of west and will be back to their camp after walking 13 km.