Height of a HillDate: 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/ |
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