Answer:
The boat has move 572.93 meters
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