L ii
i i
i i
i i
i i A
i i
i i
i i
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i i 4000 miles
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E ii
right triangle have to find side EL.
The range of a lighthouse is the maximum distance at which its
light is visible. In the figure, point A is the farthest point from
which it is possible to see the light at the top of the lighthouse L.
The distance along Earth s is the range. Assuming that the radius
of Earth is 4000 miles, find the range of Marblehead Lighthouse.
To find the range of the Marblehead Lighthouse, we need to calculate the distance EL.
Let's break down the information we have:
- The radius of the Earth is given as 4000 miles.
- Point A is the farthest point from which the light at the top of the lighthouse is visible.
- We need to find the distance EL, which represents the range of the lighthouse.
To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this scenario, the hypotenuse is the line segment AL, which represents the range of the lighthouse. The other two sides of the right triangle are AE and EL.
To find the length of AE, we need to subtract the radius of the Earth (given as 4000 miles) from the total length of AL (the range).
Once we have the length of AE, we can apply the Pythagorean theorem to solve for EL.
Let's summarize the steps to find the range of the Marblehead Lighthouse:
1. Find the length of AE by subtracting the radius of the Earth (4000 miles) from the range.
2. Use the Pythagorean theorem to find the length of EL.
By following these steps, we can determine the range of the Marblehead Lighthouse.