Question

Jane's school is due west of her house and due south of her friend Norma's house. The distance between the school and Norma's house is 8 kilometers and the straight-line distance between Jane's house and Norma's house is 9 kilometers. How far is Jane's house from school? If necessary, round to the nearest tenth.

Answer 1

Distance = 4.1 km

Step-by-step explanation

Let the distance between Jane's house from school be x

The distance can be calculated using pythagora's theorem

`\begin{gathered} \text{Hypotenus}^2=opposite^2+adjacent^2 \\ \text{Hypotenus = 9km, opposite = 8km and adjacent = x km} \\ 9^2=8^2+x^2 \\ \text{Isolate x}^2 \\ 81=64+x^2 \\ \text{Collect the like terms} \\ 81-64=x^2 \\ 17=x^2 \\ \text{Take the square roots of both sides} \\ \text{x = }\sqrt[]{17} \\ \text{x = 4.1 km} \end{gathered}`

Therefore, the distance between Jane's house from school is 4.1 km