I don't understand you work, except the first angle. Now you determine the other angle in that outer triangle. From that you should use law of cosines to solve for the slant height from the inner point to the top of tower.
60/sintop angle=innerslantheight/sin17
solve for innerslant height.
Now you have height of tower in
h/slantheight=sin21
and solve for height h.
From a point A on level ground, the angle of elevation to a water tower is 17°. From point B, 60 m nearer the tower, the angle of elevation to the top is 21°. Find the height of the tower to the nearest metre. [90m]
What I've done:
<C = 180 - (17+21)
<C = 142°
SinC/c = SinA/a
a = Sin17(60/Sin142)
a = 28.4934
Sin21 = h/a
Sin21 = h/28.4934
h = 28.4934(Sin21)
=10.2
What am I doing wrong?
2 answers
what you are doing wrong is ignoring the cotangent function.
If you check your diagram, you will see that the height h is found using
h cot17° - h cot21° = 60
h = 90.1 m
If you check your diagram, you will see that the height h is found using
h cot17° - h cot21° = 60
h = 90.1 m