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From a certain point, the angle of elevation to the top of a church steeple is 10 degrees. At a point 100m closer to the steeple, the angle of elevation is 20 degrees. What is the height of the steeple?

micheala950831  Mar 28, 2017
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Here, DC is the height of the steeple.

 

The angle next to angle B = 180º - 20º = 160º

So the remaining angle in that triangle = 180º - 160º - 10º = 10º

So this is an isocolese triangle. (I just spent about 10 minutes typing an answer before I realized this....sighh...)

That means that AB = BD.

BD = 100 m

 

sin = opposite / hypotenuse

sin 20º = DC / 100

100sin20º = DC

34.202 meters ≈ DC

hectictar  Mar 28, 2017

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