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

Algebra ->  Trigonometry-basics -> 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      Log On


   

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) About Me  (Show Source):
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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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The distance from the base of the lighthouse to point A horizontally in the southern direction is

    d%5BA%5D = 100%2Ftan%2835%5Eo%29 = 100%2F0.70021 = 142.8143 meters.


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

    d%5BB%5D = h%2Ftan%2822%5Eo%29 = 100%2F0.404026 = 247.5088 meters.


d%5BA%5D  and  d%5BB%5D  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%5BA%5D  and  d%5BB%5D. To find the distance between A and B, apply
the Pythagorean theorem

    distance from A to B = sqrt%28d%5BA%5D%5E2+%2B+d%5BB%5D%5E2%29 = sqrt%28142.8143%5E2+%2B+247.5088%5E2%29 = 285.756 meters.


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

Solved.