We can regard the ladder, the floor and the house wall as forming a right angled triangle with the ladder representing the hypotenuse.

Using Pythagoras' Theorem and letting H be the height of the ladder then,

10

H = √75 = 9.21954 (5dp)

As the answer is required to the nearest hundredth, then the rule for rounding off numbers is :-

"If the first figure to be discarded is 5 or more then the preceding figure is increased by 1".

As the first figure to be discarded is "9" (as this measures thousandths) which is greater than 5, then the preceding figure of 1 is increased by 1 to become 2.

Then H = 9.22 (2dp)

Using Pythagoras' Theorem and letting H be the height of the ladder then,

10

^{2}= 5^{2}+ H^{2}H^{2}= 100 - 25 = 75H = √75 = 9.21954 (5dp)

As the answer is required to the nearest hundredth, then the rule for rounding off numbers is :-

"If the first figure to be discarded is 5 or more then the preceding figure is increased by 1".

As the first figure to be discarded is "9" (as this measures thousandths) which is greater than 5, then the preceding figure of 1 is increased by 1 to become 2.

Then H = 9.22 (2dp)