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

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(13200) (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.

RELATED QUESTIONS
Multi-Step Problem. You can use the method described below to approximate the distance... (answered by stanbon)

a pyramid found in central america has a square base measuring 932 feet on each side and... (answered by ikleyn)

The boy scouts are going in a 20km hike.after hiking 6 1/3km on the first hour and 5... (answered by Cromlix)

Of the members of a Boy Scout troop, 15% have received the first aid merit badge. If 40... (answered by ikleyn)

Of the members of a boy scout troop,m 15% have received their first aid badge. If 40 boy... (answered by stanbon)

Of the members of a Boy scout troop, 15% have received the First Aid merit badge. If 40... (answered by stanbon)

A surveyor is measuring the distance across a small lake. He has set up his transit on... (answered by Theo)

A shaded circle is inside a square with one side of the square measuring 2" and the... (answered by Earlsdon)

On a canoe and camping trip, a group of Scouts decided to canoe downriver, set up camp,... (answered by Boreal,greenestamps)