Question

At summer camp, the swimming course runs the length (L) of a small lake. To determine the length of the course, the camp counselors measure the two "dry" legs of a right triangle. What is the length in meters of the swimming course in the figure below? A right triangle overlaps a lake. It has sides 25 and 40 meters. Hypotenuse labeled L goes through the lake.

Answer 1

Answer:

The length of the swimming course is 47.16 meters.

Explanation:

It is given that the right triangle overlaps the lake and hypotenuse L runs through the length of the lake. Thus length of the lake will be the length of this hypotenuse.

The instructors have conducted measurements of the right triangle and has found the legs to be 25 and 40 meters. The sum of squares of base and height of  a right triangle gives the value of its hypotenuse according to Pythagoras theorem.

Thus $h^2+b^2=H^2$

b - base

h - height.

$40^2+25^2=1600+625=2225$

$H=\sqrt{2225}=47.16 m$