As observed from the top of a lighthouse, 42 m high above sea level, the angle of depression of a ship sailing directly towards it changes from 30° to 45°. The distance travelled by ship during the period of observation is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 42( - 1).
In triangle ABC,
tan 45° = 42/BC
BC = 42
In triangle ABD,
tan 30° = 42/(42 + CD)
= 42/(42 + CD)
42 = 42 + CD
CD = 42 - 42
CD = 42( - 1)