A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees. At some later time, Luis takes another measurement and finds the angle of depression to the boat (now at point B) to be 39 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.

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07-06-2022
Mathematics

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A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees. At some later time, Luis takes another measurement and finds the angle of depression to the boat (now at point B) to be 39 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.

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MaheshpatelvVTidn MaheshpatelvVTidn · Answer 1 · 2022-06-16T12:12:43-04:00

The distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees.

From the above information, we can draw a right-angle triangle.

Let's suppose the distance between point A and point B is x

In right-angle triangle, BCD

tan31 = DC/BC = 107/BC

BC = 107/tan31

BC = 178.07 ft

In right-angle triangle, ACD

tan20 = DC/AC

tan20 = 107/(x + BC)

Plug the value of BC

tan20 = 107/(x+178.07)

x + 178.07 = 293.980

x = 115.91 ft

Thus, the distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.

Learn more about trigonometry here:

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What is trigonometry?

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