For the following question, what is the value of x to the nearest tenth?
A circle is shown with a chord that measures x. A right triangle is formed by chord X, a chord to the center of the circle with a measurement of 3, and the radius of the circle that measures 6.5.
(1 point)
Responses
3.6
3.6
5.8
5.8
11.5
11.5
14.3
To solve for the value of x, we can use the Pythagorean theorem.
The radius of the circle (6.5) is the hypotenuse of the right triangle formed. One of the legs of the triangle is x (the chord), and the other leg is 3 (the chord to the center of the circle).
Using the Pythagorean theorem, we have:
x^2 + 3^2 = 6.5^2
x^2 + 9 = 42.25
x^2 = 42.25 - 9
x^2 = 33.25
Taking the square root of both sides, we get:
x ≈ √33.25
x ≈ 5.8 (rounded to the nearest tenth)
Therefore, the value of x to the nearest tenth is 5.8.