Two landmarks find distance without going in water

Question

Two landmarks are in opposite sides of a lake And are facing each other. You have been asked to find the distance between the landmarks; however, you can only use distance in the land. Describe a method for finding distance and justify the use of your method. 

Answer 1

Hi AmH, let A be a point on one side of the lake. Let O be a point on the opposite side of the lake. One process we can use is to place a third point, call it B, on the same side of the lake as point A.

 

Measure the distance from point A to point B.

 

Measure the angles ∠BAO and ∠ABO.

 

Now knowing two angles, we can find the size of the third angle ∠AOB (remember, the angles in a triangle equal 180 degrees.)

 

Then we can use the trig relationship of angle, side, angle to find the distance from point A to point O using the law of Sines.

 

Questions?