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?
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