Question

solve for x to the nearest tenth.

Explanation:

Step1: Apply Pythagorean theorem

Let's consider the right - triangle formed. The hypotenuse of the right - triangle with sides 6 and $x$ is related to the other right - triangle. First, find the length of the hypotenuse of the right - triangle with sides 6 and $x$ using the Pythagorean theorem. Also, consider the large right - triangle with sides 7 and 10. The length of the hypotenuse of the large right - triangle is $\sqrt{7^{2}+10^{2}}=\sqrt{49 + 100}=\sqrt{149}$. The length of the hypotenuse of the small right - triangle with sides 6 and $x$ is also part of the large right - triangle's structure. By the Pythagorean theorem, for the small right - triangle, if the hypotenuse of the small right - triangle is $h$, then $h^{2}=x^{2}+6^{2}$, and for the large right - triangle $h^{2}+7^{2}=10^{2}$. So $x^{2}+6^{2}+7^{2}=10^{2}$.

Step2: Simplify the equation

$x^{2}+36 + 49=100$. Then $x^{2}+85 = 100$. Subtract 85 from both sides of the equation: $x^{2}=100 - 85=15$.

Step3: Solve for $x$

Take the square root of both sides: $x=\sqrt{15}\approx3.9$.

Answer:

$3.9$