Answer:
As per the statement:
The angle of depression of a boat at sea from a 100 foot lighthouse is 20 degrees.
We draw the figure for this problem as shown below:
Height of the lighthouse(BC) = 100 foot
Angle of depression = 20 degrees.
Since, angle of depression is equal to the angles of elevation
i.e, [tex]\angle DCA = \angle CAB = 20^{\circ}[/tex]
using tangent ratio:
[tex]\tan \theta = \frac{\text{opposite side}}{\text{adjacent side}}[/tex]
Here,
Opposite side = BC = 100 foot
Adjacent side = AB
Angle of elevation: [tex]\theta = 20^{\circ}[/tex]
Substitute these to solve for AB:
[tex]\tan 20^{\circ} = \frac{100}{\text{AB}}[/tex]
or
[tex]\text{AB} =\frac{100}{\tan 20^{\circ}}[/tex]
[tex]\text{AB} =\frac{100}{0.36397023426}[/tex]
Simplify:
AB = 294.375362123 foot
Therefore, the distance to the boat approximately is 294.4 foot
