SOLUTION: The angles of elevation of the top of a tower from the points P and Q at distances of 'a' and 'b' respectively from the base of the tower and in the same straight line with it a

Algebra ->  Trigonometry-basics -> SOLUTION: The angles of elevation of the top of a tower from the points P and Q at distances of 'a' and 'b' respectively from the base of the tower and in the same straight line with it a      Log On


   

Question 735049: The angles of elevation of the top of a tower from the points P and Q at distances of 'a' and 'b' respectively from the base of the tower and in the same straight line with it are complementary.What is the height of the tower?
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
And let Q be at a distance of b from the tower making an angle alpha


Let P be at distance a from the tower. This will make an angle %2890-alpha%29
Let height of tower be h



Tan%2890-alpha%29=h/a
Cot alpha=h/a
Tanalpha=a/h
Tan %28alpha%29 = h/b
a%2Fh=+h%2Fb
h%5E2=+ab

h=+sqrt%28ab%29