Question 1203415
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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?
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<pre>
The distance from the base of the lighthouse to point A horizontally in the southern direction is

    {{{d[A]}}} = {{{100/tan(35^o)}}} = {{{100/0.70021}}} = 142.8143 meters.


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

    {{{d[B]}}} = {{{h/tan(22^o)}}} = {{{100/0.404026}}} = 247.5088 meters.


{{{d[A]}}}  and  {{{d[B]}}}  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  {{{d[A]}}}  and  {{{d[B]}}}. To find the distance between A and B, apply
the Pythagorean theorem

    distance from A to B = {{{sqrt(d[A]^2 + d[B]^2)}}} = {{{sqrt(142.8143^2 + 247.5088^2)}}} = 285.756 meters.


Rounding to the nearest meter, we get the <U>ANSWER</U>:  the distance from A to B is 286 meters.
</pre>

Solved.