From the top of a lighthouse 55ft above sea level, the angle of depression to a small boat is 11.3 degrees. How far from the foot of the lighthouse is the boat?
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55/d = tan 11.3
d = 55/tan11.3 = 275 feet
An doserver in the window of the lighthouse is 32 meters above the level of the ocean. The angle of depression of the boat is 27° how far is the boat from the lighthouse
To find the distance from the foot of the lighthouse to the boat, we can use trigonometry, specifically the tangent function.
Let's assume the distance from the foot of the lighthouse to the boat is represented by 'x'. The angle of depression (θ) is the angle between the horizontal line (sea level) and the line of sight from the top of the lighthouse to the boat.
In this case, we have the opposite side (the height of the lighthouse) and the adjacent side (the distance from the foot of the lighthouse to the boat). Therefore, we can use the tangent function:
tan(θ) = opposite side / adjacent side
tan(11.3°) = 55ft / x
To solve for x, we rearrange the equation:
x = 55ft / tan(11.3°)
Now we can calculate the value of x by plugging the values into a calculator:
x ≈ 301.45ft
Therefore, the boat is approximately 301.45 feet away from the foot of the lighthouse.