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 .

Step-by-step 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,

$\tan 44\textdegree=\frac{AB}{BC}\\\\\tan 44\textdegree=\frac{1000}{BC}\\\\BC=\frac{1000}{\tan 44\textdegree}\\\\BC=1035.53\ feet$

Now, Consider, ΔABD,

$\tan 29\textdegree=\frac{AB}{BD}\\\\\tan 29\textdegree=\frac{1000}{BD}\\\\BD=\frac{1000}{\tan 29\textdegree}\\\\BD=1804.04\ feet$

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 .