An observer in a lighthouse 350 feet above sea level observes two ships directly offshore. The angles of depression to the ships are 𝛽 = 7° and 𝜃 = 9.5°.

Answer 1

I assume you want to know the distance between the boats. (The actual question is missing)

If you draw a line to the boat in question, it forms a right triangle with the vertical height of the lighthouse and the distance to the ship in x. The angle at the boat will be equal to the angle of declination from the light house as these are alternating interior angles (given that you draw a horizontal line from the light house parallel with the x axis)

The relation of the light house height (opp) with the horizontal distance to the boat (adj) is the tan of the angle:

h/d₂ = tanθ , so d₂ = h/tanθ or hcotθ d₁ = hcotβ and d between boats is d₂-d₁

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