SOLUTION: An observer 9m horizontally away from the tower observes its angle of elevation to be only one half as much as the angle of elevation of the same tower when he moves 5m nearer towa

Algebra ->  Trigonometry-basics -> SOLUTION: An observer 9m horizontally away from the tower observes its angle of elevation to be only one half as much as the angle of elevation of the same tower when he moves 5m nearer towa      Log On


   

Question 1170273: An observer 9m horizontally away from the tower observes its angle of elevation to be only one half as much as the angle of elevation of the same tower when he moves 5m nearer towards the tower. How high is thr tower? Use sine or cosine law
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
If draw the described figure, and if not follow the expectation to use Law Of Cos or Law Of Sin but use tangent and its double angle formula instead,

x and 2x the angles of elevations;
h, the tower height

system%28h%2F9=tan%28x%29%2Ch%2F4=tan%282x%29%29

h%2F4=%282tan%28x%29%29%2F%281-tan%5E2%28x%29%29
subst. for tan(x):

h%2F4=%282%28h%2F9%29%29%2F%281-%28h%2F9%29%5E2%29
.
.
highlight%28h=3%29

(not been rechecked)