I know the answer to the following question. Having a problem with the diagram.

Question

I know the answer to the following question. Having a problem with the diagram. My questions are in red. Please answer my questions, because I am very confused. I know the answer, having a problem getting to the correct answer. Thank you.

A plane flies from base camp to lake A, a distance of 280 km at a direction of 20.0° north of east. After dropping off supplies, the plane flies to lake B, which is 190 km and 30.0° west of north from lake A. Graphically determine the distance and direction from lake B to the base camp. (Do this on paper. Your instructor may ask you to turn in this work.) First determine the x- and y- distances to lake A from BaseCamp x, = 280cos(20°)-263.114 km y280sin(20°)-95.766 km y2 190 sin 30 X2 190 cos 30 = 164.54 km Now determine the x- and y- distances to lake B from lake A. I know the answer but why is x2 sin and y2 cos., I thought adj to the angle is cos and opposite the angle is sin. Is the diagram correct? d2 = 190 km Lake A x2190 sin(30°)-95 km Iputx as cos ½ = 190 cos(30°)= 164.55 km and y as sin d1 = 280 km y1 280 sin 20 x1 280 cos 20 = 263.11 km Now to determine x- and y- distances from Base Camp to lake B... xfinal = x1-x2-168.114 km yfinal -yl +y2-260.316 km Base Camp Now to know the distance from lake B to Base Camp...you use the pathagorean theorem distance = Y(Xinal)2 +(y-*)-309.88 km

Explanation / Answer

from base point to the lake A

the components of the velocity with respect to the x axis (horizontal)

x1 = s1 cos theta , y1 = s1 sin theta

x1 = 280*10^3 cos 20 = 263113.93382 m

y1 = 280*10^3 sin 20 = 95765.640 m

s1 is displacement given = 280 km from base camp to the lake A

and from lakeA to lake B

the velocity components with respect to x axis is

x2 = s2 cos (90+theta) = s2 sin theta

y2 = s2 sin (90+theta) = s2 cos theta

given s2= 190 km

x2 = 190*10^3 sin30 m = 95000 m

y2 = 190*10^3 cos30 m = 164544.8267190 m

now from base camp to lake B

X = x1-x2 , y = y1+y2

X = 263113.93382- 95000 m = 168113.93382 m

Y = 95765.640 +164544.8267190 m = 260310.466719 m

the magnitude is  

R = sqrt( x^2+y^2)

R = sqrt( 168113.93382^2+260310.466719^2) m = 309877.13 m

the direction is  

theta = arc tan (260310.466719/168113.93382) = 57.144 degrees

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