A lighthouse keeper at the top of a 120 feet tall lighthouse with its base at sea level spots a small fishing boat. The angle of depression is 5°. What is the horizontal distance between the base of the lighthouse and the boat? Round to the nearest foot.

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

- The height of the lighthouse is the side opposite to the angle of

So we can write:

where in this situation,

opposite = height of the lighthouse = 120 ft

Therefore, the length of the adjacent side is

So, the distance between the boat and the base of the lighthouse is 1372 ft.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared