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.

x ≥ 18 is your answer

step-by-step explanation:

let "a number" = x

(2/3)x + 17 ≥ 29

isolate the variable (x). do the opposite of pemdas (parenthesis, exponent (& root), multiplication, division, addition, subtraction).

first, subtract 17 from both sides.

(2/3)x + 17 (-17) ≥ 29 (-17)

(2/3)x ≥ 29 - 17

(2/3)x ≥ 12

next, multiply 3/2 to both sides to isolate the x

(3/2)(2/3)x ≥ 12(3/2)

x ≥ 12(3/2)

simplify. multiply, then divide

x ≥ (12 * 3)/2

x ≥ (36)/2

x ≥ 18

x ≥ 18 is your answer

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