Question

What is the difference between Sophia and Trisha? If necessary round to the nearest 10th.

Answer 1

Given:

DIstance between Diego and Sofia = 3 feet

Distance between Trisha and Diego = 9 feet

Let's find the distance between Sofia and Trisha.

If Sofia is straight behind Diego and directly to the left of Trisha, the figure below represents this situation:

We can see the figure forms a right triangle.

To find the distance between Sofia and Trisha, apply Pytrhagorean Theorem:

`c^2=a^2+b^2`

Where:

c is the hypotenuse = 9 feet

a is the shorter leg = 3 feet

b is the longer leg = x feet.

Let's solve for b.

We have:

`\begin{gathered} 9^2=3^2+b^2 \\ \\ 81=9+b^2 \\ \\ b^2=81-9 \\ \\ b^2=72 \end{gathered}`

Take the square root of both sides: