Question

From the lighthouse 1000 ft above sea level the angle of depression to boat a is 29 degress.a little bit later the boat moved closer to the shore b and the angle of depression measures 44 degrees.how far has the boat moved in that time

Answer 1

Answer: The boat moved 768.51 feet in that time .

Explanation:

Since we have given that

Height of the lighthouse = 1000 feet

Angle depression to boat 'a' = 29°

Angle of depression to shore 'b' = 44°

Consider ΔABC,

`\tan 44\textdegree=(AB)/(BC)\\\\\tan 44\textdegree=(1000)/(BC)\\\\BC=(1000)/(\tan 44\textdegree)\\\\BC=1035.53\ feet`

Now, Consider, ΔABD,

`\tan 29\textdegree=(AB)/(BD)\\\\\tan 29\textdegree=(1000)/(BD)\\\\BD=(1000)/(\tan 29\textdegree)\\\\BD=1804.04\ feet`

We need to find the distance that the boat moved in that time i.e. BC

so,

`DC=BD-BC\\\\CD=1804.04-1035.53\\\\CD=768.51\ feet`

Hence, the boat moved 768.51 feet in that time .