Question

Which measurement is closest to the shortest distance in miles from Natasha's house to the library?

Answer 1

Given:

The objective is to find the shortest distance between house and library.

Consider the given triangle as,

Here, A represents the house, B the grocery and C the library.

Since it is a right angled triangle, the distance between the house and the library can be calculated using Pythagoras theorem.

`\text{Hypotenuse}^2=Opposite^2+Adjacent^2`

Apply the given values in the above formula,

`\begin{gathered} AC^2=17^2+0.9^2 \\ AC^2=289+8.1 \\ AC^2=297.1 \\ AC=\sqrt[]{297.1} \\ AC=17.237\text{ miles} \end{gathered}`

If Natasha walks through Grocery store,

`\begin{gathered} AC^(\prime)=AB+BC \\ AC^(\prime)=0.9+17 \\ AC^(\prime)=17.9\text{ miles} \end{gathered}`

By comparing the two ways, ACHence, the hypotenuse distance AC, between house and library is the closest distance.