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.

.25

step-by-step explanation:

3. (5x + 1) - (-10x + 6)

simplify the answer choice. combine like terms. remember to distribute the negative to the terms inside the second parenthesis. also remember that two negatives = one positive, and one of each sign = negative.

- (-10x + 6) = + 10x - 6

simplify. combine like terms:

5x + 1 + 10x - 6

5x + 10x + 1 - 6

15x - 5

∴ it is your answer

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