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HINT: Draw a diagram.

Note: Not to scale

. . . . {x} - - - - - - - - - - - - - - - ->

. . . . .|.|.\ 34° ← angle of depression

. . . . .|.|θ \

. . . . .|.| . . \

30 . . |.| . . . \

. . . . .|.| . . . . \

. . . . .|.| . . . . . \

. . . . .|.| . . . . . . \

. . . . .|-|---------------\

. . . . . . . . x . . . . .

Remember that complementary angles add up to 90°. Use the angle of depression to find θ.

θ = 90° - 34° = 56°

. . . . {x} - - - - - - - - - - - - - - - ->

. . . . .|.|.\ 34° ← angle of depression

. . . . .|.| . \

. . . . .|.| ↑ . \

30 . . |.| . 56° \

. . . . .|.| . . . . \

. . . . .|.| . . . . . \

. . . . .|.| . . . . . . \

. . . . .|-|---------------\

. . . . . . . . x . . . . .

Remember that tan = sin / cos = opposite / adjacent.

Using 56° as the reference angle:

opposite = x

adjacent = 30

Set up the proportion.

tan(56°) = x / 30

Cross-multiply.

tan(56°) * 30 = x * 1

44.4768291 = x

x ≈ 44.5 (rounded to the nearest tenth)

ANSWER: The boat is about 44.5 m away from the lighthouse.

I got 16 and yes i took the time to do it!lol.

solve : sin34/10 = sin56/x that will yield your answer. x=distance, sorry i don't have a calc.

tan34 = x/30

30(tan34) = x

x = 20.24m