Question

Jack is deep-sea diving with two friends. Arianna is floating on the surface 7 meters above Jack, and Nicholas is exploring a coral reef 7 meters in front of Jack. How far apart are Arianna and Nicholas? If necessary, round to the nearest tenth.

Answer 1

Answer: 9.9

Step-by-step explanation:

Answer 2

Answer:

$7\sqrt{2}$ meters

Step-by-step explanation:

The first step would be to draw a picture.  We can then see that the three people are positioned in a right triangle.

Each leg of the triangle is 7 meters, and the distance between the Arianna and Nicholas is the hypotenuse of the right triangle.

This means that this distance can be solved for using the Pythagorean Theorem: $a^{2}+b^{2} =c^{2}$, where a and b are the legs of the triangle and c is the hypotenuse.

By plugging in numbers, we can see that:

$7^{2} +7^{2} =c^{2}$

The left side of the equation can be simplified

49+49

98=c^2

This means that $c=\sqrt{98}$ --> to undo the c squared, you take the square root of the whole equation

This radical can be simplified by breaking 98 into its square factors

$\sqrt{98}= \sqrt{7*7*2} = \sqrt{7^{2}*2} =7\sqrt{2}$ meters

*and remember units on the end :)