SOLUTION: The Boy Scouts of America have a method for measuring the distance across a stream: 1. Locate an object on the far side of the stream; a rock, for example (A). 2. Push a stick into

Algebra ->  Triangles -> SOLUTION: The Boy Scouts of America have a method for measuring the distance across a stream: 1. Locate an object on the far side of the stream; a rock, for example (A). 2. Push a stick into      Log On


   

Question 1149637: The Boy Scouts of America have a method for measuring the distance across a stream: 1. Locate an object on the far side of the stream; a rock, for example (A). 2. Push a stick into the ground directly across the stream from the rock (B). 3. Walk along the shore at a right angle to AB. Take any number of paces, for example 50. Mark that point with a stick (C). 4. Continue walking along the shore in the same direction for the same number of paces. (In this case, 50 more.) Mark this point with a stick (D). 5. Walk away from the stream at a right angle to BD. When you can sight a straight line directly over stick C to rock A, stop and mark your spot (E).6. Measure DE to find the width of the stream. Explain how this method works.
Answer by greenestamps(13367) About Me  (Show Source):
You can put this solution on YOUR website!


When the instructions are followed, BC and CD are congruent, and CDE and CBA are both right angles.

When you can sight A directly over C, angles ACB and EDC are congruent.

Then triangles ABC and EDC are congruent by angle-side-angle.

AB and DE are corresponding parts of those congruent triangles.

So the width of the stream AB, is the same as the length of DE.