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The angle of elevation of the top of a tower is 27 degrees from point A due east of it. The angle of elevation of the top of the tower is 11 degrees from another point B due south of the tower. Find the height of the tower if the distance AB is 40m.

Divide the base in half by putting a perpendicular line in the center.

Let the length of one base to the bottom of this line be x.

This makes the length of the other base be 40-x.

Let the height be y.

The equations known are tan(27 degrees) = y/x and tan(11 degrees) = y/(40-x).

These two can both be solved for y, giving

y = x * tan(27 degrees) and y = (40-x) * tan(11 degrees).

These two equation can be set equal to each other, x can then be solved for,

and then y can be found. I would use one equation to find a value for y

and then use the other equation to make sure it checks.

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