Answer:
1372 feet
Step-by-step explanation:
The horizontal distance between the lighthouse and the boat, the height of the lighthouse and the distance boat-lighthouse keeper form a right triangle, of which:
- The distance between keeper and boat is the hypothenuse
- The horizontal distance between boat and base of the lighthouse is the side adjacent to the angle of [tex]\theta=5^{\circ}[/tex]
- The height of the lighthouse is the side opposite to the angle of [tex]\theta=5^{\circ}[/tex]
So we can write:
[tex]tan \theta = \frac{opposite}{adjacent}[/tex]
where in this situation,
opposite = height of the lighthouse = 120 ft
Therefore, the length of the adjacent side is
[tex]adjacent = \frac{opposite}{tan \theta}=\frac{120}{tan 5^{\circ}}=1372 ft[/tex]
So, the distance between the boat and the base of the lighthouse is 1372 ft.
