SOLUTION: Due south of the base of a 100m tall lighthouse on level ground is a point A. The angle of elevation from point A to the top of the lighthouse is 35 degrees. Due east of the lighth

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Question 1203415: Due south of the base of a 100m tall lighthouse on level ground is a point A. The angle of elevation from point A to the top of the lighthouse is 35 degrees. Due east of the lighthouse is another point B. The angle of elevation from point B to the top of the lighthouse is 22 degrees. What is the distance from point A to point B?
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
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Due south of the base of a 100m tall lighthouse on level ground is a point A.
The angle of elevation from point A to the top of the lighthouse is 35 degrees.
Due east of the lighthouse is another point B.
The angle of elevation from point B to the top of the lighthouse is 22 degrees.
What is the distance from point A to point B?
~~~~~~~~~~~~~~~~~~~~~~~~~~~ 

The distance from the base of the lighthouse to point A horizontally in the southern direction is

     =  =  = 142.8143 meters.


The distance from the base of the lighthouse to point B horizontally in the eastward direction is

     =  =  = 247.5088 meters.


  and    are the legs of a right angled triangle.
The distance between points A and B is the hypotenuse of the right-angled triangle
with the legs    and  . To find the distance between A and B, apply
the Pythagorean theorem

    distance from A to B =  =  = 285.756 meters.


Rounding to the nearest meter, we get the ANSWER:  the distance from A to B is 286 meters.

Solved.



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