Question 1181848: In a flooded area, Cora is stranded at a point 70° west of north with respect to the central base of rescue operations. The nearest rescue boat is docked 40° east of north with respect to the central base. If the boat is 100 m away from the central base and Cora’s location is 75° west of north with respect to the boat, then how far away is the boat from where Cora is?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Draw this on the coordinate axis where O is the center.
A is where she is, 70 degrees W of north, which makes the AOW (W for west) angle 20 degrees. That makes AON 70 degrees, where N is due north. That is given.
OB is the line on which the rescue boat is located, and that is 40 degrees east of north so that BON is 40 degrees.
X is where the boat is on line OB, so that XA is in the direction of 285 deg, or 75 degrees west of north. That is also given.
Therefore AXO is 65 degrees, because AXB is 75 + 40 degrees or 115, and XB is a straight line going to O.
That makes the triangle of concern AXO, with angle O 110 degrees, and AXO (angle X) 65 degrees. So angle A must be 5 degrees.
-
We want AX which is opposite to the angle of 110 degrees.
so AX/sin 110=100/sin 5, since the boat is 100 m away from O.
AX=sin 110*100/sin 5
=1078.2 m
|
|
|
