Question

One of the legs of a right triangle measures 12 cm and its hypotenuse measures 14 cm.Find the measure of the other leg. If necessary, round to the nearest tenth.

Answer 1

Concept

Name the sides and apply the Pythagoras theorem to find the third side.

Opposite = 12 cm

Hypotenuse = 14 cm

Adjacent = m

`\begin{gathered} \text{Pythagoras theorem} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \end{gathered}`

Next,

Substituting opposite and hypotenuse to get the adjacent.

`\begin{gathered} \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ 12^2+m^2=14^2 \\ 144+m^2\text{ = 196} \\ \text{Next, collect like terms} \\ m^2\text{ = 196 - 144} \\ m^2\text{ = 52} \end{gathered}`

Find the square root of both sides

`\begin{gathered} \sqrt[]{m^2}\text{ = }\sqrt[]{52} \\ m\text{ = 7.211} \end{gathered}`

Final answer

Other leg = 7.2 cm