Answer:
x ≈ 11.1
Step-by-step explanation:
We can see that the radius of the diagrammed circle is 17.4. Keep this in mind for later.
We are given a length of 16.2 for part of a chord (a line segment whose two ends are on the circumference of the circle). We know that 16.2 is half the total length of the chord because the chord is perpendicular to the radius.
Therefore, the length of the longer leg of the right triangle is also 16.2 because it is the other half of the chord.
Using this deduction, we can solve for the length of the shorter leg of the triangle using the Pythagorean Theorem.
a² + b² = c²
16.2² + b² = 17.4²
b² = 17.4² - 16.2²
b = [tex]\sqrt{17.4^2 - 16.2^2[/tex]
b ≈ 6.35
We can see from the diagram that x and the shorter leg of the triangle add to the radius, whose length we identified earlier as 17.4.
So, we can subtract the length of the shorter leg of the triangle to solve for x.
x = r - b
x = 17.4 - 6.35
x ≈ 11.05
x ≈ 11.1
