Question

Find the value of x. If necessary, write your answer in simplest radical form.2416XX(Simplify your answer. Type an exact answer, using radicals as needed.)

Answer 1

In a right-angled triangle, the Pythagoras theorem holds:

$\text{Hypothenus}^2=opposite^2+adjacent^2$

We are given :

Hypothenus = 24

opposite = 16

adjacent = x

Substituting and simplifying, we have:

$\begin{gathered} 24^2=16^2+x^2\text{ } \\ x^2\text{ = 320} \\ x\text{ = }\sqrt[]{64\text{ }\times\text{ 5}} \\ x\text{ = 8}\sqrt[]{5} \end{gathered}$