Question

as observed from the top of lighthouse 150 m high above the sea level the angle of depression the angke of depression of a ship sailing directly towards it changes from 45 to 60 determine the distance travelled by the ship during the period of observation​

Answer 1

Step-by-step explanation:

Let AB be the lighthouse and the two ships be at point C and D respectively.

⇒ In △ABC,tan45

o

=

BC

AB

⇒ 1=

BC

150

∴ BC=150m

⇒ In △ABD,tan30

o

=

BD

AB

⇒

3

1

=

150+CD

150

⇒ 150

3

=150+CD

⇒ CD=150(

3

−1) m=109.5 m (Take

3

=1.73)

∴ The distance between two ships is 109.5m