Question

The diagram shows jib PQ of a crane.$PQ=20m$ . Find the height $QR$ when the reach $PR$ is $12m$

Answer 1

Finding the height

Given : $PQR$is right angled triangle where angle $R$ is right angled

So,

By Pythagoras theorem,

$$\begin{gathered} \Rightarrow {\left(PQ\right)}^2={\left(PR\right)}^2+{\left(QR\right)}^2 \\ \Rightarrow {\left(20\right)}^2={\left(12\right)}^2+{\left(QR\right)}^2 \\ \Rightarrow {\left(QR\right)}^2={\left(20\right)}^2-{\left(12\right)}^2 \\ \Rightarrow {\left(QR\right)}^2=400-144 \\ \Rightarrow QR=\sqrt{256} \\ \therefore QR=16m \end{gathered}$$

Hence, the height $QR$ is$16m$.