A boat observes the top of a cliff to be at an angle of elevation of 25 degrees. The cliff is also at a bearing of W 30 degrees N from the boat. The boat then travels 100 meters in a straight path. The boat then observes the cliff to be due north, with an angle of elevation of 15 degrees. Using this sufficient information, calculate the height of the cliff.

height: h; initial distance from boat: d1; final dist from boat d2; boat travel dir: alpha; solve for h

Assuming cliff is at 300 degrees (clockwise from N) from boat's  initial location (but using E as x-axis and all angles measured counter clockwise),

(1) h = sin( 25/180*pi ) * d1

(2) h = sin( 15/180*pi ) * d2

(3) d2 = d1 sin( 150/180*pi ) + abs( 100 sin( alpha ) )

(4) d1 cos( 150/180*pi ) = 100 cos( alpha )

4 variables, 4 independent equations, solving for h...

cliff height is 42.776 meters.  Or, did I miss something? Ok, the abs( ) is a bit ugly but we are calculating distances, and there are too many significant digits, but who cares...

Posted by Erik on 2006-05-21 08:11:32