Answer:
x = 6.6 cm
Step-by-step explanation:
The angle formed on the circle by the radius and the tangent is right.
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides.
Hypotenuse is (x + 8.45) and 2 sides are x and 13.5, thus
(x + 8.45)² = x² + 13.5² ← expand left side
x² + 16.9x + 71.4025 = x² + 182.25 ( subtract x² from both sides )
16.9x + 71.4025 = 182.25 ( subtract 71.4025 from both sides )
16.9x = 110.8475 ( divide both sides by 16.9 )
x ≈ 6.6 cm
