Question

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 1

Step-by-step explanation

Lets first graph the situation:

Using the sine law for x, we have:

`(x)/(sin(15°))=(50)/(sin(75°))`
`x=(50sin(15°))/(sin(75°))`
`x\approx13.39746`

And for y:

`(y)/(sin(22°))=(50)/(sin(68°))`
`y=(50sin(22°))/(sin(68°))`