Height of a Hill

Date: 09/06/97 at 11:44:48
From: susruta
Subject: Trigonometry

From the top of a hill, the angles of depression of two consecutive 
kilometre stones due east are 30 and 45 degrees, respectively. Find 
the height of the hill.

Thank you.       

Susruta

Date: 09/12/97 at 15:30:02
From: Doctor Rob
Subject: Re: Trigonometry

The diagram will look like this:

  P
  -...-------------------D
  | `-.``--..
  |    `-.   ``--..
  |       `-.      ``--..
  .----------`-----------``-
  C          A     1k      B

P is the top of the hill, A and B are the kilometer stones.
Angle DPB is 30 degrees, angle DPA is 45 degrees, and distance AB 
is one kilometer. You want to find PC, the height of the hill.

Since when a transversal cuts parallel lines PD and CB, the opposite
angles are equal, you know that angle CBP is 30 degrees and angle CAP
is 45 degrees.  Then AC = PC/tan(45), and BC = PC/tan(30), and
BC - AC = 1 km.

  1 = PC/tan(30) - PC/tan(45)

Now solve for PC.

-Doctor Rob,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/