Question

Determine the unknown side length of the right triangle to the nearest hundredth. View the figure.

Answer 1

In the right triangles whose legs are a, b and its hypotenuse is c

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

In triangle JLK

∵ LK and JL are the legs of the triangle

∵ KJ is the hypotenuse

`\therefore(LK)^2+(JL)^2=(KJ)^2`

∵ KL = 14 m and KJ = 18 m

Substitute them in the rule above to find JL

`\begin{gathered} (14)^2+(JL)^2=(18)^2 \\ 196+(JL)^2=324 \end{gathered}`

Subtract 196 from both sides

`\begin{gathered} 196-196+(JL)^2=324-196 \\ (JL)^2=128 \end{gathered}`

Take a square root for both sides

`\begin{gathered} \sqrt[]{(JL)^2}=\sqrt[]{128} \\ JL=11.3137085 \end{gathered}`

Round it to the nearest hundredth

`\therefore JL=11.31m`

The answer is 11.31 m