# From the top of a lighthouse 55 ft 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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To find the distance from the foot of the lighthouse to the boat, we can use trigonometry. The angle of depression from the top of the lighthouse to the boat forms a right triangle with the height of the lighthouse (55 ft) and the distance from the foot of the lighthouse to the boat (which we'll call ( d )).

Using the tangent function, we have:

[ \tan(\text{{angle of depression}}) = \frac{{\text{{opposite side}}}}{{\text{{adjacent side}}}} ]

Plugging in the values we know:

[ \tan(11.3^\circ) = \frac{{55}}{{d}} ]

To solve for ( d ), we rearrange the equation:

[ d = \frac{{55}}{{\tan(11.3^\circ)}} ]

Calculating this value gives us the distance from the foot of the lighthouse to the boat.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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