Answer:
SN = √29 cm = 5.39 cm (2 dp)
Explanation:
Using the given information, we can create a new right triangle with hypotenuse SN, then use Pythagoras' Theorem to find the length of SN.
Extend the line SU to the left until it is under point N → label this point P. Connect point P to point N. This creates a new right triangle (see attachment).
If BU = 4 cm, and M is the midpoint of BU, then UM = 2 cm
⇒ PN = UM = 2 cm
As NM = 2, then PU = 2 cm
⇒ PS = PU + US = 2 + 3 = 5 cm
Therefore, the two legs of the right triangle with SN as its hypotenuse are 2 cm and 5 cm.
Using Pythagoras' Theorem:
⇒ a² + b² = c²
⇒ 2² + 5² = SN²
⇒ 4 + 25 = SN²
⇒ SN² = 29
⇒ SN = √29 cm = 5.39 cm (2 dp)