Pre-calculus (Trigonometry)

The rotating spotlight from the Coast Guard ship can illuminate up to a distance of 250 m. An observer on the shore is 500 m from the ship. HIs line of sight to the ship makes an angle of 20 degrees with the shoreline. What length of shoreline is illuminated by the spotlight?

(This is how far I have gotten)

sinA = sinB
----- -----
a b

sinA sin20
---- = -----
500 250

sinA = 500(sin20)
---------
250

sinA = 43 degrees

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  1. the ship is 500 sin 20° = 171 m from shore.

    A beam of 250m will illuminate 2√(250^2-171^2) = 365 m of shoreline.

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  2. Thank you

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