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

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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