Question

find the value of x.

x≈
(do not round until the final answer. then round to the nearest tenth as needed.)

Explanation:

Step1: Apply the Pythagorean theorem

In a circle, if a radius is perpendicular to a chord, it bisects the chord. Let the radius be \(r=x\), one leg of the right - triangle be \(a = 4\), and the other leg be \(b=5.7\). According to the Pythagorean theorem \(a^{2}+b^{2}=r^{2}\).
So, \(x^{2}=4^{2}+5.7^{2}\).

Step2: Calculate the value of \(x\)

First, calculate \(4^{2}=16\) and \(5.7^{2}=32.49\).
Then \(x^{2}=16 + 32.49=48.49\).
Take the square root of both sides: \(x=\sqrt{48.49}\approx6.96\).
Rounding to the nearest tenth, \(x\approx7.0\).

Answer:

\(7.0\)