Question

For the final exam in a scuba diving certification course, Karl navigates from one point in a lake to another. Karl begins the test x meters directly beneath the boat and swims due south for 8 meters. He then turns due east and swims 24 meters, at which point he swims directly from his location, in a straight line, back to the boat. If the distance that Karl swims back to the boat is 26 meters, what is the value of x?

Answer 1

Answer on Question#40051 - Math - Geometry

For the final exam in a scuba diving certification course, Karl navigates from one point in a lake to another. Karl begins the test x meters directly beneath the boat and swims due south for 8 meters. He then turns due east and swims 24 meters, at which point he swims directly from his location, in a straight line, back to the boat. If the distance that Karl swims back to the boat is 26 meters, what is the value of x?

Solution:

Using Pythagoras' theorem:

$\Delta BCD$

$$B D ^ {2} = B C ^ {2} + C D ^ {2}$$ $$B D ^ {2} = 8 ^ {2} + 2 4 ^ {2} = 6 4 0$$

$\Delta ABD$

$$x ^ {2} = A D ^ {2} - B D ^ {2}$$ $$x ^ {2} = 2 6 ^ {2} - 6 4 0 = 3 6$$

So $x = 6$

Answer: value of $x$ is $6\mathrm{m}$