Question

Two boats are observed by a parasailer 75 meters above a lake. The angles of depression are 12.5° and 79. How far apart are the boats?

Answer 1

Answer:

The two boats are 323.72 m apart.

Step-by-step explanation:

See the attached diagram.

B is the point of observation and AB is the height of the parasailer i.e. 75 m.

Now, from the right triangle Δ ABC,

$\tan 79^{\circ} = \frac{AB}{AC} = \frac{75}{AC}$

⇒ AC = 14.58 meters.

Again, from the right triangle Δ ABD,

$\tan 12.5^{\circ} = \frac{AB}{AD} = \frac{75}{AD}$

⇒ AD = 338.30 meters.

Hence, CD = AD - AC = 338.30 - 14.58 = 323.72 m

Therefore, the two boats are 323.72 m apart. (Answer)