Question

solve for x to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem to left - hand triangle

Let the hypotenuse of the left - hand right - triangle with legs 3 and 5 be $a$. Then $a=\sqrt{3^{2}+5^{2}}=\sqrt{9 + 25}=\sqrt{34}$.

Step2: Apply Pythagorean theorem to large right - triangle

In the large right - triangle, one leg is $a=\sqrt{34}$ and the other leg is $x$, and the hypotenuse is 9. Using the Pythagorean theorem $a^{2}+x^{2}=9^{2}$. Substitute $a = \sqrt{34}$ into the equation: $34+x^{2}=81$.

Step3: Solve for $x$

Subtract 34 from both sides of the equation: $x^{2}=81 - 34=47$. Then $x=\sqrt{47}\approx6.9$.

Answer:

$6.9$