Question

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

Answer 1

To obtain the measure of the other leg of the right triangle, the following steps are necessary:

Step 1: Draw a sketch of the right triangle and label it with the dimensions provided in the question, as below:

Step 2: Apply the Pythagorean theorem to obtain the measure of the other leg of the right triangle, as follows:

The Pythagorean theorem goes as follows:

`\text{hypothenus}^2=\text{opposite}^2+\text{adjacent}^2`

Thus:

`\begin{gathered} 14^2=12^2+x^2 \\ 196=144+x^2 \\ 196-144=x^2 \\ 52=x^2 \\ x^2=52 \\ x=\sqrt[]{52}=7.21 \\ x=7.2\text{ (to the nearest tenth)} \end{gathered}`

Therefore, the measure of the other leg of the right triangle is 7.2cm