40 points! precalculus no cheating! dont get the answer from a diff website and then c& p! i need a full detailed explanation!

The boat has move 572.93 meters

Step-by-step explanation:

Remark

The first thing you need to do is draw a diagram. Please do that. My answer will make no sense without one. None of the programs I have will do will draw an adequate diagram.

Angles of depression are the complements of the angles that you need to solve this problem. You need to draw the diagram so you can put in the complements or so you can see what I'm referring to.

Step One

Find the complement of 14.52

Comp 1 = 90 - 14.52

comp 1 = 75.48

Comp 2 = 90 - 45.1

Comp 2 = 44.9

Step Two

Draw these on your diagram. Call the distance you seek = x. Call the remaining distance to the lighthouse = y

Step Three

Find the distance represented by x + y

Tangent = opposite / adjacent

tan(75.48) = (x + y)/200         Multiply both sides by 200

200*tan(75.48) = x + y           Switch sides

x + y = 200* tan(75.48)

x + y = 772.23

Step 4

Find the value of y

tan(44.9) = opposite / adjacent  

The opposite  = y

tan(44.9) = y / 200          Multiply both sides by 200

200 * tan(44.9) = y          switch sides

y = 200*tan(44.9)            Multiply the factors on the right

y = 199.303

Step 5

Find x

x + y = 772.23 from step 3   Substitute the value for y from step 4

x + 199.303 = 772.23            Subtract 199.303 from both sides

x = 772.23 - 199.303            Collect terms on the right

x = 572.93

2