Question

question
solve for $x$. leave your answer in
simplest radical form.
answer
attempt 1 out of 2
$x = $

Explanation:

Step1: Find the height of the large right - triangle

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\). Let the height be \(h\). For the large right - triangle with hypotenuse \(c = 10\) and base \(a = 9\), we have \(h=\sqrt{10^{2}-9^{2}}\).

$$h=\sqrt{100 - 81}=\sqrt{19}$$

Step2: Use the Pythagorean theorem for the small right - triangle

For the small right - triangle with one leg \(h=\sqrt{19}\) and the other leg \(4\), and hypotenuse \(x\). By the Pythagorean theorem \(x=\sqrt{(\sqrt{19})^{2}+4^{2}}\).

$$x=\sqrt{19 + 16}=\sqrt{35}$$

Answer:

\(x=\sqrt{35}\)