Question

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Two boats are traveling toward a lighthouse that is 200 feet (ft) above sea level at its top. When the two boats and the lighthouse are collinear, the boats are exactly 250 feet apart and the boat closest to the lighthouse has an angle of elevation to the top of the lighthouse of 15°, as shown.

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What is the value of x, rounded to the nearest hundredth?

Answer 1

Which Number Is x, You Didnt Specify

Answer 2

We can see here that the value of x, rounded to the nearest hundredth, is 746.55 ft.

To find the value of x, we can use trigonometry and the given information.

Let's consider the right triangle formed by the boat closest to the lighthouse, the lighthouse itself, and the vertical line from the boat to the top of the lighthouse.

The height of the lighthouse is 200 ft, and the angle of elevation from the boat to the top of the lighthouse is 15°. We can use the tangent function to find the value of x.

tan(15°) = opposite / adjacent

The opposite side is the height of the lighthouse (200 ft), and the adjacent side is x.

tan(15°) = 200 / x

To solve for x, we can rearrange the equation:

x = 200 / tan(15°)

x = 200/0.2679 = 746.547

x ≈ 746.55 ft (rounded to the nearest hundredth)

Therefore, the value of x, rounded to the nearest hundredth, is approximately 746.55 ft.