Jon P. answered • 07/10/15
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Unless I'm missing something, there's extraneous information in the problem, which is often given to force you identify the information that really matters.
In this case, you know that B is 100 m from the tower and that the top of the tower has an elevation of 26 degrees. It doesn't matter what B's bearing is, or what the angle of elevation from A is.
The line from B to the base of the tower, the tower, and the line from B to the top of the tower form a right triangle. Relative to the angle of elevation, the tower is the opposite side, and the line from B to the base is the adjacent side. Since you know the angle and the length of the adjacent side, use tangent to find the opposite side:
tan 26° = (height of tower) / 100
100 tan 26° = height of tower
100 * 0.488 = height of tower
48.8 m is the height of the tower.
Michael P.
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07/10/15
Jon P.
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Sorry Michael, you're absolutely right. I misread the problem.
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07/10/15
Michael P.
Hey Jon - all good. Did you get 42.4 or 42.24? Maybe I shouldn't be fussing about the 0.16 difference!! All good - thanks so much again for your help. Good to know I've got a place to come to for some tricky problems! Cheers, Michael
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07/10/15
Christine L.
The answer is 42.4. Solve[(h/tan26)^2=h^2+100^2-2(h)(100)(cos60),h] as the side OA = height of tower (45 deg triangle) and the side OB is h/tan(26), OA =100
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07/25/21
Michael P.
07/10/15