Answer: x is 40
Explanation:
Since line AB is a radius and line CB is the tangent line. Hence, angle ABC is a right angle. OR
From radius tangent theorem, which states that " the angle between a tangent and a radius is 90°. We can then conclude that, triangle ABC is a right angle triangle, with angle ABC equal to 90°.
We can determine the unknown side x using the Pythagorean theorem which states that " the square of the longest side that is, hypotenuse equals sum of squares of the other two sides"
Side AC is the hypotenuse.
Therefore,
/AC/² = /AB/² + /CB/²
But /CB/ = x
Therefore,
/AC/² = /AB/² + x²
From the question
/AC/= 41
/AB/ = 9
Hence,
41² = 9² + x²
1681 = 81 + x²
x² = 1681 - 81
x² = 1600
x = √1600
x = 40
Hence, x is 40