17. An observer at the top of a 50m lighthouse sights a boat out at sea at an angle
of depression of 15°. A short while later, the same boat is at an angle of
depression of 22° along the same line of sight. To the nearest meter, how far
did the boat travel?
A 6 m
B 7 m
C 20 m
D 63 m

The image is attached with the answer below we can see the two boats at different angles 3 so the distance between the two boats will be calculated as:-

Distance of the boat at an angle of 22 degrees.

[tex]x_1 =\dfrac{50}{tan22}=123\ m[/tex]

Distance of the boat at an angle of 15 degrees.

[tex]x_2=\dfrac{50}{tan15}=186\ m[/tex]

So the distance between the two boats will be:-

x₂-x₁ = 186 - 123 = 63 m

Hence the distance between the two boats will be equal to 63 meters.

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17. An observer at the top of a 50m lighthouse sights a boat out at sea at an angle of depression of 15°. A short while later, the same boat is at an angle of depression of 22° along the same line of sight. To the nearest meter, how far did the boat travel? A 6 m B 7 m C 20 m D 63 m

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17. An observer at the top of a 50m lighthouse sights a boat out at sea at an angle
of depression of 15°. A short while later, the same boat is at an angle of
depression of 22° along the same line of sight. To the nearest meter, how far
did the boat travel?
A 6 m
B 7 m
C 20 m
D 63 m