Answer:
The 51.39 feet far is the boat from the lighthouse .
Step-by-step explanation:
Now by using the trignometric identity.
\(cot\theta = \frac{Base}{Perpendicular}\)
As given
The angle of depression from the top of a lighthouse to a boat in the water is 30°.
If the lighthouse is 89 feet tall .
As shown in the figure given below.
\(\theta = 30^{\circ}\)
Base = AC = 89 feet
Perpendicular = CB
Put in the identity .
\(cot 30^{\circ} = \frac{89}{CB}\)
\(cot\ 30^{\circ} = 1.732\)
Put in the above
\(CB= \frac{89}{1.732}\)
CB = 51.39 feet (Approx)
Therefore the 51.39 feet far is the boat from the lighthouse .
