SOLUTION: a river has parallel banks which run directly east-west.Kylie takes a bearing to a tree on the opposite side. The bearing is 47degrees true. She then walks 10m due east, and take

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Question 633404: a river has parallel banks which run directly east-west.Kylie takes a bearing to a tree on the opposite side. The bearing is 47degrees true. She then walks 10m due east, and take sa second bearing to the tree. This is 305 degrees true.Find:
a. her distance from the second measuring point to the tree.
b. the width of the river, to the nearest metre
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
a river has parallel banks which run directly east-west.
Kylie takes a bearing to a tree on the opposite side.
The bearing is 47 degrees true.
he then walks 10m due east, and takes a second bearing to the tree.
This is 305 degrees true.
:
Drawing a diagram of this will help a lot
;
Find the interior angles of the triangle formed by the 1st meas point (A),
the 2nd meas point (B), and the tree (C)
A = 90 - 47 = 43 degrees
B = 305 - 270 = 35 degrees
C = 180 - 43 - 35 = 102 degrees
:
Find:
a. distance from the second measuring point to the tree.
let a = this distance, use the law of sines
a%2Fsin%2843%29 = 10%2Fsin%28102%29
a%2F.682 = 10%2F.978%0D%0A.978a+=+.682%2A10%0D%0Aa+=+%7B%7B%7B6.82%2F.978
a = 6.97 meters from the tree to the 2nd meas point
:
b. the width of the river, to the nearest meter
A right angle triangle formed by a perpendicular of the near side river bank
and the tree, this is the dist across the river (d).
find the interior angle at the tree
180 - 90 - 35 = 55 degrees
Use the cosine of 55 here
cos(55) = d%2F6.97
.57*6.97 = d
d ~ 4 meters across the river