Answer:Answer: x = 2.55
Step-by-step explanation: We will start off with triangle CBD, since it has two sides with known values.
In triangle CBD, the hypotenuse is 6 units (it's facing the right angle).
Using the Pythagoras theorem, CB² = CD² + BD²
6² = CD² + 4.2²
36 = CD² + 17.64
Subtract 17.64 from both sides of the equation
18.36 = CD²
Add the square root sign to both sides of the equation
√18.36 = CD
CD = 4.28 (approximately 4.3)
We can now solve for x in triangle ACD.
The hypotenuse is 5 (because it's facing the right angle)
Using the Pythagoras theorem
AC² = CD² + AD²
5² = 4.3² + x²
25 = 18.49 + x²
Subtract 18.49 from both sides of the equation
6.51 = x²
Add the square root sign to both sides of the equation
√6.51 = x
2.55 = x
Therefore, x = 2.55