Question

Vicky’s house is due west of Seaside and due south of Oxford. Seaside is 39 miles from Vicky’s house and 89 miles from Oxford. How far is Oxford from Vicky’s house, measured in a straight line? Pythagorean Theorem

Answer 1

80 miles

Explanation:

A diagram representing the given problem is attached below:

The distance from Oxford to Vicky's house is labeled x in the diagram.

To find the value of x, we make use of the Pythagorean Theorem.

`\begin{gathered} \text{Hypotenuse}^2=\text{Opposite}^2+\text{Adjacent}^2 \\ \implies89^2=39^2+x^2 \end{gathered}`

We solve for x.

`\begin{gathered} x^2=89^2-39^2 \\ x^2=(89-39)(89+39) \\ x^2=50*128 \\ x^2=6400 \\ x^2=80^2 \\ \implies x=80 \end{gathered}`

The distance from Vicky's house to Oxford is 80 miles.