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17. An observer at the top of a 50m lighthouse sights a boat out at sea at an angleof depression of 15°. A short while later, the same boat is at an angle ofdepression of 22° along the same line of sight. To the nearest meter, how fardid the boat travel?A 6 mB 7 mC 20 mD 63 m

Answer :

Explanation

Lets first graph the situation:

Using the sine law for x, we have:

[tex]\frac{x}{sin(15°)}=\frac{50}{sin(75°)}[/tex][tex]x=\frac{50sin(15°)}{sin(75°)}[/tex][tex]x\approx13.39746[/tex]

And for y:

[tex]\frac{y}{sin(22°)}=\frac{50}{sin(68°)}[/tex][tex]y=\frac{50sin(22°)}{sin(68°)}[/tex][tex]undefined[/tex]

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